I play a lot against level 5 Stockfish, sort of as a way to play against an opponent I know is much better than me while I learn from computer analysis against itself.
I just started this game, where I quickly got up 3 pawns:
I don't know where to go from here. I've been watching some of John Bartholomew's beginner videos, but this is such a weird position compared to when I'm used to (regular King's / Queen's Pawn opening) that I just have no idea how to proceed and exploit my material advantage. What's a good way to think about capitalizing when you're ahead like this?
If you don't see an immediate win or a way to win even more material safely, play natural moves. Just develop your pieces normally, take over the center, and get your king to safety. In this position you'll consider Nf3, d4, 0-0, Nc3, etc. If you have a lasting material advantage, tactics will emerge eventually.
If you're up three pawns, just play on. You don't need to exploit a material advantage with tactics or a mating attack; on the contrary, your opponent will find it hard to defend, trade off material slowly and eventually you'll be in an endgame three pawns up and should win with if you have the minimum of technique.
A win is a win, be it in 30 moves or 130. Don't be afraid to win in endgames, that's exactly what a material advantage lets you do most easily.
Yes as the previous posters already said you don't need to do anything special. Just keep your focus when you are up material and play moves that defend you well and that stop any incentive or possible play from your opponent.
You don't always have to find the most accurate move. Just moves that don't lose you anymore pieces and simple moves that stop your opponents pieces. Eg.. not allowing rooks on open files, preventing a knight from getting to a good outpost, blocking in a bishop.
When you're ahead in material, play as if you weren't. Simply continue making good moves. Oftentimes when somebody is up material they try to force exchanges while giving their advantage away. If you're ahead in material (with no compensation for your opponent), attack your opponent with your extra material. That will make them want to trade pieces into a losing endgame. If your opponent has some compensation it's possible you will have to return some material to not get mated.
You did well. If you are one or more pawns up, trade pieces, go to an endgame, create a passed pawn, queen it.
If you are a piece or an exchange up, attack.