I've got a cycled 2.5 gallon on my desk at work - looking at it right now as I practice my touch-typing, as a matter of fact... (So damned s-l-o-w! This post may take me 20 minutes to finish!)
lauraleellbd covered all the correct points. Set your tank up exactly as you want it (except for the fish, of course), and add some ammonia. Two separate colonies of bacteria will develop in the gravel and filter. The first will eat ammonia and excrete nitrites. The second will eat nitrites and excrete nitrates. Live plants and partial water changes are use to keep the nitrates (which are much less harmful to your betta than ammonia or nitrites) at safe levels.
An accurate test kit is essential. Add enough ammonia to get between 5 and 10 ppm and keep it at that level until it drops almost to zero in a 24-hour period. Then test for nitrites (they'll probably be very high until the second type of bacteria gets established). Keep adding ammonia, too (you don't want the first colony to starve).
Eventually you'll get zero readings for both ammonia and nitrites. Be patient - it may take a while. This means you're cycled and converting 100% of them into nitrates. Then do one large water change (maybe 75%) and add your fish. His waste (and any uneaten food) will supply the ammonia from now on.
Plants aid the process, and should be added right from the beginning. A great way to "jump start" the cycling is to borrow a used filter and some gravel from an already-cycled tank. Both will already contain both kinds of bacteria. All they have to do then is migrate into your gravel and filter. This method reduced the cycling process to a week or two.
It's work and it takes patience, but it's so worth it, and so much better for your betta!
And (I hope this is OK, mods) if you haven't yet, check out www.ultimatebettas.com
. It's a great site with some very helpful, knowledgeable people (kinda like here...)