Here is a basic link on how to do a fishless cycle:http://www.wikihow.com/Do-a-Fishless-Cycle
To deal with the nitrite, you need to build up a colony of bacteria that will convert your nitrite to nitrate. This does take some time, and is a little slower to proliferate than the initial colonization of the bacteria used to oxidize your ammonia, converting it to nitrite.
Nitrite and ammonia are both toxic to snails. I recommend frequent water changes and minimal feeding, until your tank naturally cycles. If you can get your hands on some filter media from a cycled and mature tank, you can seed your own filter and speed up the process. I wouldn't solicit a local fish store for their media, as it can contain harmful/parasitic organisms.