I can help you do a fish-in cycle, since it's what I did. A lot of people don't recommend this, since it can be stressful/potentially lethal to a betta if you're not on top of things.
First things first, you will definitely need a test kit. There is an API master test kit for about $36 at Petsmart, I think. A little expensive, but well worth your money and it will last a long time. Testing strips are cheaper, but not accurate.
Baisically you will have to test your water everyday to check the ammonia levels (and nitrite once the ammonia is done with) and do small, frequent water changes. I was doing at least 30% a day when I was cycling mine. Sometimes I would have to change another 30% during the night or in the middle of the day. Just remember to check the levels often and do small water changes when needed! Again, don't do 100% changes because you will lose the cycle.
To help speed up the cycling process, you can get filter media (the stuff you find inside the filter), gravel, or decorations from a tank that's already cycled. It helps A LOT.
I used water and a bit of sponge from my uncle's tank when I was cycling, and the process was done in a little less than two weeks! Go to a pet store and see if they're willing to give you anything for it.
Again, don't use any chemicals! The only thing you should be using is water conditioner, which treats tap water. Anything that claims to help cycling, clean water, or anything like that is total bogus unforunately.
For now, I would suggest keeping the tank in the warmest room in your house.