Okay, it is entirely possible to do a fishless cycle. Basically, what you'll need to do is set up your bigger tank (most people agree that a 5g is the minimum for easy cycling), set up your heater and your filter and all that good stuff, and put in your conditioned tap water.
Two things before we get started, one, ALWAYS condition your tap water before adding it to a cycling or cycled tank. Failing to do this will kill your cycle, or stop a cycle that is starting. Second, you're going to need a Master Liquid Test Kit. Strips are crap, don't waste your money. The kit is expensive, but to do this right, you're going to need it. And, they last for months and months and months, so it's not like something you're going to have to replace every three days. :)
Now, you're going to need to either add in fish food (which is going to rot and create ammonia), or you're going to need to add pure ammonia, which is apparently avail from most hardware stores.
From there, you are going to change the water ONLY when your ammonia readings come up to 0.25 to 0.5ppm. Then do a 50% change, and retest to make sure that the ammonia has come down. You still want SOME ammonia, the ammonia is what your good bacteria is going to eat.
After awhile, you'll notice that your ammonia starts to go down, and your nitrITE starts to go UP. This is good, you are getting there! :)
Continue to do your water changes to keep the nitrITE at reasonable levels, and eventually you'll start to see nitrATE. (this is the day you have a massive party. ;)
You are fully cycled when your tank hits 0 ammonia, 0 nitrITE, and between 5-20ppm of nitrATE. Once that holds stable for a few days or a week, you are good to add fishies. :)
Here is, by far, the best and easiest site I found about cycling a tank. I couldn't figure out how it all worked until I found this place, and then it clicked. :)
And...then there's the cheater method. Some people say it works, some people say it doesn't...I've been successful with it.
To do the Cheater Method, you have your fish already in your tank, life is good, leave them in there about a week. Your ammonia is going to get to about 0.25 (so you should be doing a water change), but, DON'T change the water, you're going to NEED that ammonia.
Now, you're going to go out and buy some Bacteria in a Bottle. I've always used the API Quick Start, it's worked great for me, but I've also seen rec's for a Seachem brand, and for Dr. Tims One and Only. Follow the package directions.
I don't know how the Tims or the Seachem work, but the API should only need to be added once (you can add more for some days, it won't hurt anything, but my guys were good with just one dose). Just make sure you've got some ammonia in there for the BB's to live off of before you put it in. Also, just get a small bottle, unless you are starting several hundred gallons worth of fish tanks. ;) Once the bottle has been opened, for whatever reason, the bacteria in there are only viable for about 24-48 hours, after that, they die...or something, because it doesn't work any more. (I had multiple tanks I was cycling with this stuff, and the ones done immediately after opening cycled no problem, but the one I waited a week to start would not cycle until I bought a new bottle of Quick Start.)
So, there you go. Cycling in a nutshell. :)