Sasha
The main idea of fishless cycling is instead of the fish providing the ammonia (via their poo!

) it is supplied via another source
ie. Pure, unpurfumed, unanything ammonia.
at a certain rate (see link above) until it hits the level stated (sorry, i haven't read the topic for while, and can't remember the levels stated

) at which point you half the doseage, as too much ammonia will then hamper the growth of the benficial bacteria, as opposed to helping it.
I have also heard adding fish food to the tank, as if there were fish in it, that also helps the fishless cycle along.
you still do water changes, and eventually the nitrItes will spike, and then the nitrAtes will spike and nitrItes and ammonia should go to zero.
The length of time this can take will depend on the tank and various other factors.
If you still have your original tank running, you can help the new tank along by squeezing the filter into your new tank, or exchanging some of the gravel, plants or rock (the beneficial bacteria grows on anything in the tank).
Hope this helps and good luck with the new tank
Neil