1. to act (a part); to play (a role)
そうして初めて、僕は本当に役を演じることが出来る。Only then can I truly play the role.
2. to perform (a play, etc.); to put on (a production)
ならばこの舞台、全力でもって演じなければならない。In that case, I must perform on this stage with all my might.
3. to commit (e.g. a blunder); to disgrace oneself; to do something conspicuously; to make a scene
4. to pretend (e.g. to be a good father)
お前、本当はわざと馬鹿を演じているんだろう？You're actually playing the fool on purpose, aren't you?