How do you study opening theory using Stockfish? Any tips to be up to date with recent opening theory?
Usually, computers are not very accurate in the openings. I'd suggest using a good database of grandmaster games like Chessbase or Chess365. If you're trying to prepare against somebody or against a variation I'd recommend using Chessbase while running an engine. For example:


e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 a6 5. Nc3 Nf6 6. Be3 e5 7. Nb3 Be6 8. f3 h5 9. Nd5 Bxd5 10. exd5 Nbd7 11. Qd2 11... g6 12. O-O-O 12... Nb6 was the position I was preparing against. 


The main line goes 13. Qa5 Bh6 14. Bxh6 Rxh6 but in many games White just gets a worse position. This is unsatisfactory, and Stockfish 6 found an improvement. 


Kb1!


If you're curious, go check out how white gets a forced advantage.