The first step in learning to read the runes is to get to know the runes themselves. This doesn't necessarily mean memorizing interpretations out of a book, although the literal meanings of the rune names should be memorized as a starting point. Instead, try taking one rune each day, starting with Mannaz and ending with Odin, and meditate on it. There are several exercises you can do daily to aid in this: word association with the rune names, visualization, physical connection with the rune, etc. I know of one coven member who made 'flash' cards to help him memorize the associations of each rune.
Always keep a record of your rune readings in a journal. Although it's not quite as easy to draw a nine rune cast as it is to record a tarot spread, do try and make the effort. Record which runes landed face up and face down, what you think each one meant in the context of the reading, and what your general impressions were. Even if a reading makes no sense to you when you do it, its meaning might become clearer later on, and this will encourage you to pay closer attention to your instincts (even if you are sure you're wrong!).
One thing I've done since I first found runes was to draw 1-3 runes each time I do a tarot reading -- I've found it adds a great deal to the reading. I record my rune readings in the same journal as my tarot.
Some books give upright and reversed meanings for the runes (like Tarot cards). This is obviously impractical if one is 'casting' the runes, since many will land sideways or at odd angles. Also, one would think that if this had been the intention of the original creators of the fuþark, they wouldn't have designed so many runes to look the same upright as inverted. I find that drawing a rune from a pouch is the best way to handle the upright and reversed issue.
The most important thing, however, is that you feel comfortable with the method you choose. If you feel the need for a more structured reading devise a pattern for that has some meaning – it will give the reading a more tangible context. If you find nine or twelve runes overwhelming, use three or four. If you want to just grab a handful and cast them, go right ahead. In my experience, the runes themselves tell you how they want to be read.
As well, runes in different sizes, shapes and materials lend themselves to different methods, and through meditation and experimentation you should be able to choose a technique that best suits both the runes' 'personality' and your own.
There are many layouts to read the runes, following is a collection of the most common.
Single Rune/One Draw
I like this layout for its simplicity, and its power. Here, the rune you draw is the general feeling and overall attitude toward the question. It also represents the outcome to your question.
Three Rune/Time Flow/Three Sisters
This layout is probably the most common layout in modern rune interpretation. It is the layout I use most often, if only to do a reading as part of my ritual note-taking (one to three times each month).
This spread is most often read from left to right. The left rune, the past, represents the past influences that brought you to your current situation, therefore it doesn't necessarily introduce new information. The center rune, the present, represents the action you should take in an effort to overcome this obstacle. Look carefully at the advice given here. If you choose to follow it, the outcome will likely lead you to the final rune. The last rune, the future, indicates where you are going and what you can shape. The future is not fixed; there are many possibilities to each situation. This rune acts as a guiding force that helps you seek the answers within yourself.
Wheel Layout
In this layout, you form a "plus" sign with five runes. The first will be the bottom of the cross and represents the basic influences that underlie the question. The second one is placed to the left of the center position and represents the obstacle to overcome. The third rune is at the top and represents beneficial processes. The fourth is to the right of center and represents the outcome of the question. The last rune is placed at the center and shows all the future influences.
It looks like:
3
2 5 4
1
The center rune represents the idea or person that is influenced by the surrounding runes. This centerpiece "selection" differentiates both layouts from the rest. A runic symbolic representation of a question differs from the more direct question you might ask when choosing the three rune layout.
Although adaptable the Wheel Layout is most useful as a method to discover more information about a specific rune. This layout adds the dimensionality of "space" to the three runes layout dimensionality of "time", the Wheel illustrates what forces are working spiritually and emotionally, influencing your situation.
See the diagram below: 
In this layout, you can imagine this new dimension as a vertical line that divides the horizontal line of time. The top of this vertical line represents the higher conscious or higher spiritual regions of the inner self. The bottom represents the "well of the unconscious" or the emotionally distressed regions of the inner self. Both polar regions are difficult to grasp in the everyday living experience, yet both empower the forces that allow this very experience. By including these regions in your layout, you are able to identify the energies that are being expressed or felt in these realms.
So, this layout provides a fourfold vision of the situation at hand by illustrating the line of time (horizontal line), and level of consciousness (vertical line) for any given situation. The center rune lies on the axis of time and level of consciousness, and represents the nature of the question or person asking the question.
For instance, if you would like to learn more about your finances, select Feuh as your center rune. If you would like to uncover more about a past experience, select Hagalaz as your representative center rune. If you just want to learn more about how a specific rune plays into your reading, select that as your center rune.
Along the line of time, the rune positioned on the left represents the past influences which have shaped your current situation. Nauthiz here, for instance, would indicated that your situation was brought about by insecurities and fears.
The rune positioned opposite, on the right, represents the future, where you are headed and what you can shape. Inguz and Jera are endearing runes to find in this positon of outcomes. They bring hope, fruition and the sense that expectations will be met.
The bottom rune represents influences that stem from the "well of the unconscious" which are always difficult to identify. The unconscious is the mysterious realm that lies deep with the psyche, where ongoing destructive and creative conflicts from past experiences reside. Because it is protected by an enormous barrier that acts to suppress these conflicts, these conflicts are seldom identifiable to the individual. In time they are likely to emerge as images in dreams or feelings of emotional anxiety.
The top rune represents the higher influences at work which will offer help and inspiration in your quest. It is the north star shining through the misty air of the heavens. This rune is most often neutral, yet in the instance of finding a reversed rune in this position, such as Raido, it would indicate that your Higher Self has been directed down the wrong path and that its powers are inaccessible at this time.
(from Aswynn, Power and Principles of the Runes, 121-123).
Runic Cross
This reading is derived from Ralph Blum himself.
Although some find his "rune interpretations" helpful in a modern psychological sense, others find his methodology of reading layouts is backwards...but what is backwards to some, is forwards to others. If you are a dedicated Blum fan, please read no further. If you are interested in seeing this six rune layout as a more detailed version of the Three Sisters, please see the diagram below:
This spread varies in interpretations, however, I suggest the following: The far left rune represents your past, while the far right rune represents what lies in the future. The bottom most rune identifies the unconscious powers at work that are continuing to influence your current situation, and the top most rune identifies the higher conscious powers at work that will act as guidance and inspiration.
The two runes that lie between the unconscious and the higher conscious indicate what is affecting your current situation at close range (your current barriers and sources of power accordingly). The lower rune represents the subconscious energies that are being brought to the surface. What has formerly been repressed or acted out unconsciously, for instance, you can now identify. The higher rune represents the active conscious energies that are within grasp. This rune identifies the personal strengths that are available to you right now. Harnessing these strengths and heeding the advice of this rune, will allow you to shape the future.
Eight Wheel
This is a layout for the experienced rune caster and comes from the wisdom of Freya Aswynn and my exposure to psychological materials.
Acting much like the Four Wheel, the Eight wheel adds yet four more dimensions of interpretation. Crisscrossing the vertical line of space, and the horizontal line of time, are the dimensions of the active future, the inactive past, the active past and the inactive future. As a helpful rough and ready psychological guide, imagine the horizontal line as the surface of the sea and consider whatever falls beneath its surface as being unknown and out of your control to change (it is the unconscious realm). Whatever lands above the surface, however, can be seen and is therefore in your control to change (it is in the conscious realm).
Please see the diagram below:
The Eight Wheel - Beginning at the points between the higher conscious and future, the active future has been added. This rune represents what you can do to handle the problem. Opposite here lies the inactive past which represents your unchangeable characteristics, or those that have not yet ripened. By inserting a point between the higher conscious and past, we see the active past. Represented here are past influences that continue to affect your psychological complex, yet are changeable. Traumas may be indicated here as well as pleasant childhood memories. Opposite here lies the inactive future, the unconscious forces, such as dreams, anxieties and suppressed materials that invade consciousness and predetermine your future.
(from Aswynn, Power and Principles of the Runes, 124-125).
(Some graphics provided by Runecast.com, which is now defunct.)
Layouts Used for Divinations
Although they are very similar, rune readings for psychological insight are different from those used in divination.
Odin's Rune
Place the Runes into a cloth pouch, and shake them up. Reach into the pouch and draw out a single Rune. Make sure when the Rune is pulled out, and you turn it over that you do not accidentally do not invert the Rune. This Rune will reveal the crux of your present situation, or the basic answer to your question.
Three Rune Spread
Place the Runes into a cloth pouch. Draw out three Runes and place them in a horizontal line in front of you. Reading from the left to the right, the positions represent:
1) You now
2) the Challenge ahead of you
3) the Best Outcome.
Read the Runes and interpret them relative to their position.
Runic Cross
Place the Runes into a cloth pouch then draw out 6 Runes and place them in the following order:
Place the first Rune in the center of your work area. This represents you now.
The second Rune goes to the right of the first Rune. This represents your past.
The third Rune goes to the right of the first Rune. This Rune represents the future.
The fourth Rune goes below the first Rune. This Rune reveals the foundation of the situation.
The fifth Rune is placed above the first Rune. This Rune is the challenge ahead of you.
The sixth Rune goes above th fifth Rune. This rune represents the best outcome.
Three Life Spread
This spread is useful for exploring past incarnations. There are five runes involved in this spread. Place the Runes into a cloth pouch, and remove five of them, placing them in the following order:
The first Rune goes on the right side of your work area. This Rune is your birth and childhood of this life.
The second Rune goes to the left of the first. This Rune represents your present.
The third Rune goes to the left of the second. This Rune is your future in this life.
The forth Rune goes below the second Rune. This Rune reveals a past incarnation.
The fifth Rune goes above the second Rune. This Rune is your future incarnation.
Interpret the Runes relative to their position and also relate them to what must be gained in each incarnation.
~from Maat’s Book of Shadows