When to Sacrifice Minor Pieces for Pawns?

The most important thing is that after the sacrifice, your pieces that are left on the board are very active. A common beginner mistake is to sacrifice their most active pieces, and then they're left with pieces that aren't doing much.

"Activity" is some combination of the following two things:

1) General mobility (influencing many empty squares)
2) Being in contact with important offensive or defensive points (often a weak pawn or king)

So let's do an example.

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First notice how white's bishops point towards the kingside, white's knights are on the kingside, and as soon as the knight on f3 moves the white queen can go to the kingside too. Also imagine we cut the board in half kingside vs queenside. Black only has 2 pieces on the kingside (rook on e8 and knight on f6). All this means that I've really stacked the deck against black. The position is ripe for a kingside attack, but how to proceed?

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So the bishop sacrifice created weakness around black's king, but most importantly, after the sacrifice, white's remaining pieces were very active.

The other typical sacrifice that comes to mind is in endgames, to make a passed pawn, but I feel like it's almost too obvious to be worth mentioning. Here's a basic example:

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But again, the sacrificed piece leaves the board so that something that is left on the board can shine. In this case the pawns.

So to reiterate, the most important thing before sacrificing is identifying which pieces (or pawns) will be very good for you. The sacrificed piece is just a support role.

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These examples showed immediate compensation for the sacrificed material... but when beginners see a GM sacrifice, sometimes it's not obvious that compensation exists. So beginners get the wrong idea and think the star of the show is the sacrificed piece, and if they sacrifice enough, then something will magically work out for them. This is one reason they typically sacrifice their good pieces and then have to resign because the pieces left on the board are doing nothing for them.

Llama47 this is all really really helpful and brilliantly explained. Thank you :)

Nice post, llama!

No, you are not. At first, I thought you were joking, but now it seems to be that you are actually serious. Sad. This also contributes nothing to this topic.

Mostly when you get a really strong attack, to win material or mate. Or could just be a positional sac to create lots of weaknesses for your opponent

A minor piece for 1 pawn is right only if it leads to checkmate or promotion.
A minor piece for 2 pawns is risky. Example:
https://www.chessgames.com/perl/chessgame?gid=1032520 
A minor piece for 3 pawns is often good. Example:
https://www.chessgames.com/perl/chessgame?gid=1098786 

Usually if you can sacrifice a piece for 3 pawns and that would lead you yo a 3-0 majority you should do it, same goes for exchange sacrifices

Really helpful folks, really appreciate it.