I am writing this post in response to a request (yes, I actually take those). I have been working diligently the last couple of weeks and this morning popped up into a 40+ second handstand without any fuss. At the risk of sounding like a motivational speaker, I wasn't always this good and I had to work very hard to become so. But, unlike a motivational speaker, I will now share with you the secret of my success.
Before you even start doing any handstand training you should have at least a base level of shoulder strength, otherwise you're trying to run before you can walk. These numbers aren't set in stone, but I would think that being able to bench press at least 135 lbs (or something similar) or complete over 30 push-ups would be a decent starting point. If you're lighter, a smaller bench and more push-ups is acceptable, and vice versa for the heavier readers.
You can complete this program by just kicking up into handstand after handstand while you fall over, and it's possible that you will eventually learn to hold it, but this is like throwing spaghetti at a wall. My method is tried and tested (on myself) and I'm positive it will work for you.
Your first step is to learn how to do a headstand. Get something very soft for your head - like one of those folding mats at the fitness center, or a couch seat cushion. Place your head on the soft item and your hands should be at least a foot to a foot and a half behind your head and roughly shoulder width apart (a triangle is what we're going for here). Next, either balance your knees on your elbows and then straighten up into the headstand, or for the more gangly or impatient of you just try kicking up against a wall or otherwise. Obviously this will put a lot of strain on your neck, so if you don't think you're up to it, then work on strengthening your neck first (various ways, perhaps that will be another post).
Once you've mastered the headstand, you can begin learning the handstand, the DFM Way. The trick is to find a lot of couch cushions, mats, etc. that you can stack up on top of each other. One idea might be a stack of text books on top of which you place a pillow. Balance in your headstand on top of your tower of books/mats (if it's a folding mat, then just fold it up)/cushions, etc. Once you've accomplished this feat then violently push yourself up into a handstand (or as close as you can get). You do not need to hold this handstand for even a second. Just pushing up hard is all that matters (note: the higher your stack, the easier this will be). Once you've pressed up, then fall over or step back down and try it again, and again, and again. Eventually, after a few days perhaps, you will improve to the point where you can push up, balance momentarily, and then lower your head back down to the start. When you can do this, work to the point where you can go up and down, up and down, for at least 8 or more reps (a rep, or repetition, is one complete cycle of up and down).
Once you have accomplished your 8+ reps, then remove one book, mat fold, cushion, etc. from your stack. Repeat the entire process. By the time you have gotten down to the ground in this fashion, you should have no problem holding a 20 second handstand or more. Good luck.