Cycling, the universal word for the Nitrogen Cycle.
Since i hope you all know what cycling is i wont go on about how to do it. I will give a few tips to make it go faster. In order from the best way to the worst (the worst way will work for some people dont worry)
1. Using cultured gravel from another tank, if the other tank has an undergravel filter it will be even better
2. Using a bacteria in a bottle product that is frozen
3. Using a bacteria in a bottle product that is room temp
Ok as you can see, there arent many ways to buy your way to faster cycling, the best way (and often the cheapest) is to get some cultured gravel, get some at your lfs
Now once you have the cultured gravel, you can do the following to speed it up even more
If your doing a fish-less cycle, get all the airstones, powerheads, filters, everything to raise the water turbulence, you can even buy some fans to blow on the water to make some ripples. Do the same for fish cycle but only do as much as the fish desires
Ok here is something that most people should know, the colder the temp, the slower bacteria multiplies. Frozen stuff has no multiplying bacteria (thats why we invented the freezer, to stop bacterial growth) but the lower the tanks temp the higher the oxygen. The higher the oxygen level the faster the bacteria multiplies. So you need to find a mid zone, if your doing a fish-less it doesnt really matter what temperature your doing, i think the best would be around 70 degrees (room temp).
For fishless dont vacuum the gravel, dont change the filter media, dont do anything except change the water when needed.
Things that might seem like a faster way to cycle, but is the same speed:
Adding more fish, raising the ammonia, and not changing the water. Adding more fish raises the bio-load and no matter how much ammonia, bacteria multiplies at the same speed. Bacteria grows on objects, the gravel, ornaments, plants, tank walls and most of all the filter. Changing the water will not take the bacteria out, and second to that, no matter how much water you take out, the fish will always poop!