I'd read the links Biev posted, they're pretty good to get you started on your way.
I personally cycled with the "in fish" method, I bought some cheap feeder minnows from a pet store and put them in the tank and fed them. I used Seachem's Stability as my source of bacteria and followed the instructions on the label. It took well over a month for my tank to cycle properly and when I added my axolotls I did have a spike in ammonia for about a week that needed constant water changes and monitoring because my filter wasn't keeping up with the new waste load the axolotls had. When I say "spike" I mean I was getting readings of .25ppm instead of 0.0, it never reached above that.
However next time I start a new tank, if I don't just use a piece of my filter media from the established tank I would do the pure ammonia method. It seems to work a lot faster since you can control the amount of ammonia you're putting in the tank to start it off. This method CANNOT be used with fish or other animals in the tank. The high concentration of ammonia at the start will kill all the animals you put in.
No matter which method you pick, just follow the instructions and you should be good to go. You know you'll be nearing the end of the cycle when you get high nitrites and nitrates but no ammonia. Just another week or so after that and you'll see zero ammonia and zero nitrites but a decent amount of nitrate. Just do weekly water changes from there on to lower the nitrates. And remember to never wash your filter or media in tap water or you'll crash your cycle and don't completely replace a filter without throwing old medium in there because that can also cause a tank to crash.
While cycling I also bought some small water plants, an anubias of some sort and an amazon sword I think. I quarantined them while the tank was cycling and added them in towards the end. Live plants can help with breaking down nitrates. I also bought some little marimo moss balls for decoration and nitrate help.