First of all, welcome to the forum. We're glad you're here; your fish is glad you're here. Before we get into cycling, you may want to make sure of your basics.
In order of importance:
---Water conditioner. Seachem Prime is recommended a lot around here as a good value. API StressCoat is also good. What kind are you using?
---A heater is very important. The one Teeny recommended is a good value. Aqueon makes a quality 50w heater, so does Hagen. Fifty-watts is not too big for a 5gal tank. Eighty degrees is about right.
---A place to hide. Some sort of decoration that he can get in or under to hide from predators. We know there aren't any, but he doesn't.
---Plants, artificial or live. To make him feel more cozy and at-home.
---Quality food. Pellets: the first ingredients listed should be fish products. Frozen bloodworms for a treat.
---Water test kit to keep an eye on your water quality. If you can't afford the whole API liquid test kit, at least get the two bottle ammonia test kit.
This is a good beginners article by one of our members: http://www.tropicalfishkeeping.com/b...are-faq-20058/
I recommend that you get used to keeping him well-fed and his water clean and ammonia free for a while---get used to the routine---before getting into the complexity of cycling.
Cycling is a little mysterious but not too hard to understand. This is a nice basic explanation of how it works: http://www.tropicalfishkeeping.com/betta-fish-care/
And this is a longer piece on how to actually do it: Aquarium Nitrogen Cycle and cycling. Methods for ammonia, nitrite removal.
Cycling with raw shrimp or fish is no longer recommended due to the risk of Saprolegnia mold. The same goes for fish food, unless done with caution.
Take your time. Get used to Betta-keeping. When you are more confident in you abilities, come back here and we'll coach you through tank cycling.