When you first begin your journey (after returning the parcel to Professor Oak) in Pokemon FireRed, you will be given the Kanto Pokedex. This Pokedex includes the 151 Pokemon Species of the Kanto Region, from Bulbasaur to Mew. However, since Pokemon FireRed was introduced during the 3rd Generation of Pokemon, there were way more Pokemon known in the World of Pokemon at the time. In total, there actually 386 Pokemon Species to be found in order to complete the National Pokedex (which, at the time, included all 1st Generation Pokemon, 2nd Generation Pokemon, and 3rd Generation Pokemon.
In order to obtain the National Pokedex in Pokemon FireRed, you must first complete a few tasks. First, you must defeat the Main Story by defeating the Elite Four and becoming the next Kanto Region Champion. After doing so, if you have caught and registered at least 60 Different Pokemon Species in your Kanto Pokedex, you will receive the National Pokedex from Professor Oak. After you do, you can officially begin to obtain 2nd Generation and 3rd Generation Pokemon.