Each Pokémon has four. You may select powers from each PKMN you have, by touch. In all, you can use only 4 powers.Meaning, even if you have 100 PKMN, you must choose from each of their abilities, using only four at a time. These may be switched by touching the PKMN whose powers you wish to switch with.
“…Judge not what a man has done, but judge what he could have done if he was a different bloke altogether. For art thou a leper? And a leper can changeth his spots…” --Rudy Wade, Misfits (Series 4, Episode 8)