Cycling a tank is giving the tank good bacteria that is necessary for most fish to survive. Most people on this forum do fishless cycling Fishless Cycling - Article at The Age of Aquariums - Tropical Fish
here is some info on it. This will not harm the fish! If you don't have a filter, you don't need to worry about cycling cuz a tank can't cycle without a filter. Cycling a tank while a fish is in it is bad because ammonia and nitrates (poisenous to fish) build up in the tank and harm the fish, most fish can't survive this, but a few like zebra danios, mollies, goldfish, and bettas usually can. Its not reccomended tho. However, you need to cycle a tank for most fish, so just do it with out fishies! :) Tetra Betta pellets will work great! 2-3 twice a da is perfect! 1g is really not that great, altho some people do keep their bettas in that, it is easier to have happier healthier bettas in atleast 2.5g of water. Heated, filtered, and cycled is best, but you don't have to do all that. If you are planning on cycling a tank, you will have to wait about 4 weeks to get the fish. Many tanks that are only a quart say they are good for bettas, but really like I said bettas do best in larger tanks. My smallest betta tank is 4 gallons. All but one of my fish tanks are cycled, and that is because filters scare one of my bettas, and he gets all stressed with them. I have never had a betta live less than 4 years, so I think that I have given you an ok idea of how to set up a betta tank. They are alot more work than it seems like!