Try visualizing, say, a thick vertical line. See it darkly in your mind's eye. Now imagine it splitting at the top and curling in opposite directions like a split hair. Try to manipulate the vision so that it does what you wish, and put it back together. Try turning various shapes into other shapes, like imagining a square turning into a circle, slowly rounding itself, or imagine a circle shrinking to a tiny dot. Visualize shapes blending or splitting, and have firmly in mind before you start what they're going to do; otherwise it's just like watching a kaleidoscope, which might be fun but is pointless for the purpose of these exercises. (This was suggested in Carl Rider's How to Improve Your Psychic Power.)
Try manipulating a symbol, such as a five-pointed star. First, firmly visualize the star, and imagine what its color is, everything about it, so that you can really see it in your mind's eye. Then, when you can see all five limbs of it, imagine it breaking out in flowers all over. When you can hold that image for a while, make the star tilt back and forth, as though it is walking. When you're ready to stop visualizing, take the flowers off and put the star back the way you first imagined it, then let it dissolve. (This exercise was also suggested by Mr. Rider.)
Try this sequence of visualizing an apple. First you must be able to see the apple in your mind's eye. Then you'll want to try to make the apple solid enough that you can see it sitting in your hand. At this point try to "visualize" it with your tactile sensations too; you should feel the weight and temperature and texture of the apple in your hand. Try and make it as real as you can; you can even eat it, and visualize everything you need to make it real like eating an apple. You may have to stop with one bite, but you may completely eat the apple as an exercise. (This was suggested in Starhawk's The Spiral Dance.)
Another one by Starhawk involves drawing a pentagram in your mind's eye with a blue line of fire. Envision the first line of an invoking pentagram (from the top point downwards to the bottom left point), and watch it be drawn in the air. Hold it after it's finished, then start at the bottom left point and go upward, making the lines disappear.
Here is a more complex one, suggested in Mr. Rider's book. Choose a Tarot card from the Major Arcana, and study it. You may want to prepare for this exercise a few days in advance by choosing your Tarot card and leaving it in a prominent place for you to notice now and then. When the time comes for you to try your visualization, prop the card up in front of you, close down all the lights, and light one candle to illuminate the card, preferably in a place where you don't see the candle, just its light. Now ground and center yourself, focus on steady breathing, and relax, now and then looking at your card but not staring at it. Finally, when you can call a pretty detailed version of the card into your memory without looking, close your eyes and start. Imagine the card in front of you growing larger and larger, until it is the size of a large screen inside you, something bigger than yourself, like a doorway you can step through. Take a deep breath and step over the edge of the card into the realm shown. Now wander into the card, looking at your surroundings. Don't necessarily go into the card with an idea of what you want to do; let it happen naturally. Look around you, and don't go beyond the horizon of the card. Most Major Arcana cards picture at least one person; you may choose to talk to that person, or look inside a hidden box, or whatever. Do what interests you, what you might really do if you came upon a situation like this. Try to really experience it, as if in a dream, and see, hear, feel, and experience everything as if it is real. Nothing especially interesting or amazing has to happen (though it might!), but try to do something in the card and then return to the real world by backing out the way you came and stepping into reality, then making the card shrink again in front of you. Should you wish to try this with other cards at other times, feel free; just make sure you don't get lost and "pop" back out, that is very bad for visualization skills. But when you've finished the visualization, it's important to ground yourself in reality again, just slap the card face down and get up and do something mundane.
This next one is a bit different because it actually involves creating something rather than visualizing it, but it begins with visualization and requires visualization skills to keep it up. Collect a ball of energy in your hand. Bring it up from inside your body to your fingertips, feel the tingle it creates, and draw it into the center of your palm. Stare at your hand and see if you can't see a light there. Make it grow as much as you can, preferably until it fills your whole palm. Now try to manipulate it; put it down, pass it from hand to hand, touch it to your face. Energy can actually be passed through your body too, so you can attempt to control it so it does so. When you are finished, make sure to absorb it again or bury it in the floor or earth so that it isn't just freely floating, because energy is a real thing.
If you and a friend become advanced at these techniques, you can play catch with the ball of energy, and see if you can really see it as it travels through the air, and really feel it after your friend throws it to you. If you can visualize the light this way, you may be on your way to attempting to read auras or at least see them, if you haven't already.
Here is an everyday visualization you can do anywhere, anytime. Pick a point some distance from yourself and imagine that your consciousness is there, looking back at you. Visualize what a person would see from that point, and furthermore, visualize being in that point looking at yourself. What would you see? What would you see behind yourself? To extend this, try adding other senses to it, like if a woman behind you in line is talking, try to "hear" what she would sound like speaking from farther away. Or if you "project" your consciousness to another place, try making real the various feelings you would experience while standing in that place (i.e., is there a stronger draft, are you leaning against something, is there better light, et cetera).
To continue with this idea, try visualizing a place where you currently are not present but you know well. Or imagine, for instance, standing on the other side of a corner you've just passed or sitting inside a car or bus. Remember to engage all the senses, not just vision. As a variation, visualizing other places you've been to, while sitting at home or work. Or try visualizing looking at yourself in a mirror, and really see it, and really experience standing in front of that mirror.
If you're feeling really advanced, try these. Look at an object, and then try to visualize its back. (This can be anything from a block you're holding to the other side of a building.) If you can do this, try something harder: Try to visualize two familiar locations at once, and get a sense of being in BOTH places. This may sound conflicting, but try to accept the sensory input of both places. Also attempt to take in a 360º view of the world, not in a series like you would see turning your head, but all of it at once, all around.
You can try many of these things with or without a focus, as well--for instance, while on the phone with a friend, try to imagine where they are, and visualize being in that place, really seeing what your friend would. Attempting to see places you've never been or don't know well could be the beginnings of learning remote viewing, if you're interested.
Starting from the above "everyday visualization," these last few exercises were suggested by Richard of the UK, at Karnautrahl@hotmail.com (re-written with my explanations).