What it does
Psych Up has two steps: first it clears all your own current stat stage changes, then it copies the target's current stat stages onto you exactly. That's a full overwrite, not an addition. If the target has +3 Attack and -1 Speed, you end up with +3 Attack and -1 Speed — the negatives come along for the ride.
It can't be copied by Mimic, that's a hard mechanic limit.
The key doubles application: the target can be your own partner. If your partner spent two turns getting to +4 Attack via Swords Dance, you can clone that instantly with Psych Up instead of spending your own turns to build up.
Who runs it
Klefki (9% usage) uses Psych Up as part of a support-oriented set. Its ability Prankster gives status moves +1 priority, so Psych Up moves before most things — meaning Klefki can copy a boost from a setup sweeper before they even get to use their buffed attack. The limitation to remember: Prankster moves don't work on Dark-type targets.
How to use it
The cleanest line in doubles is partnering with a setup sweeper. Your partner sets up — say Dragon Dance for +1 Attack and +1 Speed — then Klefki uses Psych Up targeting that partner, instantly matching those boosts. Now two Pokémon on your side have the same stat advantage, and your opponent has to deal with double the threat.
You can also flip the direction: if an opponent has spent multiple turns stacking boosts, clone their setup instead. The trade-off is you lose any boosts you had — but that's usually a fine deal if you had none and they built up something large.
Tips & strategy
Psych Up copies the exact current stat stage state, including any negatives already on the target. Check what's actually on your intended target before using it — if Intimidate has already dropped your partner's Attack by 1, you're copying that -1 too.
This move is an opportunity cost. You're not attacking, not supporting in any other way — just transferring an existing advantage. It's worth committing to only when the target already has significant boosts built up. If the setup total is low, just attacking is almost always better use of the turn.