What are the general principles for playing hypermodern against hypermodern? I've recently discovered that I really enjoy playing 1... g6 and that it tends to give me better results as black than opening with my d or e pawns.  However, a few times now the computer opponent I play against has opened with something like 1. g3 or 1. Nf3 and proceeded in hypermodern style instead of trying to occupy the center.  I've been playing 1... g6 anyway, but I feel like I don't really know what I'm doing then—I can set up a decently defensive position the same way I would against a classic attack, but I usually end up playing super passively, probably not putting enough pressure on white.

At the level of general principles, what should I look for when playing hypermodern vs. hypermodern?  (Or, as a frame challenge, are there reasons that I should try to occupy the center myself instead?)

If it helps for context, I play what I think is just above beginner level; I can hold my own against the app on my phone when it's set to ELO 1200 (though the app doesn't say if this is calibrated to compare to a FIDE ELO, a USCF ELO or something else).

I am aware of this related question.
Good question. I personally have tried as White to avoid advancing my center pawns and fiancheto one or both my Bishops, and control rather than occupy the center. For example I opened 1.b3. My experience tells me that Black can in fact set up a pawn center and have it solidly reinforced, thus equalizing. You get a center and now you have to be careful and watchful to not miss white's breaks (or even sacrifices) blowing up that center and leaving you with weak pawns.

Choose some key squares that you want to completely control and center your game on that. For instance, let's say you want to have a pawn d5 and you focus on hindering the e4 square, not allowing White to advance his/her pawn to e4 easily. Then you'd like a knight on f6 and maybe a bishop on f5 (or g6). You may also put a rook on e-file. Similarly, you may put a pawn on e5 and control the d4 square with a knight on c6, a well-placed dark squared bishop, etc.

It is usually impossible in practice to have two pawns in the center (say both e5 and d5) and yet protect them completely. So, do not get greedy for central pushes, having one pawn that is solid is better than having two that are shaky.

If you take into account whites c-d-e-f pawn pushes and subsequent exchanges and/or closings of the center, you should be fine. Usually a central control is a big advantage, and your opponent has to do something to free their pieces. If White does not want to advance his/her e and d pawns more than 1 square, how are they going to launch any serious initiative.

So, in summary, if Whit does not want the center, go ahead and occupy it yourself. Build up a solid center with pawns protecting pawns and pieces boosting them. You'll enjoy more space behind your pawns than your opponent will behind theirs!