What it does
Protean changes the user's type to match the move it's about to use, then that move gets STAB (×1.5) because the types now match. The change happens before the move lands, so the damage calculation always includes STAB.
Gen 9 nerfed this hard: it only triggers once per switch-in now, not once per move. You get one type change per time you come onto the field. Pick wisely.
Who runs it
Greninja (87%) — base 122 Speed, uses Protean as a pure offensive tool. It's already fast enough to outspeed most things, so the type change is mostly about getting STAB on the right coverage move.
Meowscarada (66%) — base 123 Speed, naturally Grass/Dark. Its own typing already gives STAB on Grass and Dark moves, so Protean matters most for its coverage options — Triple Axel as Ice, or switching to a type that covers a specific threat.
How to use it
Decide what your first move is before you switch in. Look at what's on the opposing field, figure out what threat you need to answer immediately, and choose your first move around that.
After that first move, the type is locked for as long as that Pokémon stays on the field. Don't expect a second type change — it won't happen.
Tips & strategy
The locked type is where players get caught out. You switch in, use Night Slash to become Dark type, then the opponent brings in a Ground-type — now your Grass coverage has no STAB and your Dark typing doesn't help you. The type choice is a commitment.
Defensive Protean plays are real too: use a Water-type move first to become Water-type, and you now resist incoming Water attacks. In doubles this matters when you need to survive a specific hit to fire off your key move.
If you've played this before Gen 9, reset your expectations. The old version gave STAB on every move and was genuinely broken. The current version is strong but requires a single committed choice each time in.