Search by name
You can search for a Pokémon by name. If you only remember part of the Pokémon's name, It can still probably find it for you. It can't deal with typos right now though.
Search by number
Search by national dex number. If you want Bulbasaur, just type 1, not #001.
Search by type
Here are a few examples of how to seach by type.
fire
Search for Pokémon that have a fire as either of their types in any form (e.g. Charmander, Charizard, Rotom).
water flying
Search for Pokémon that are either water/flying (e.g. Gyarados) or flying/water (e.g. Cramorant).
grass none
Search for Pokémon that are only grass type, no 2nd type (e.g. Tangela, Chikorita, Lilligant).