That's a known problem. I asked myself the same thing, usually in similar positions in the French. I think a grandmaster would have to answer it. This is what I know:
1) If you still have the queen's bishop on c8 or d7, the e6 pawn is actually not that weak, so you can break easier.
2) Breaking is easier when white has played Nf3 rather than f4. The move f4 also costs a tempo, so you may not have to worry at all and play elsewhere. 1...f6 2.exf6 gxf6 weakens the kingside and it leaves the e5 square in the pliers d4 and f4. While this is still playable you cannot do it when white has ueberdeckt the e-file. If you do not play gxf6 obviously e5 is a real weakness, so you have to play that very carefully and not exchange into an endgame. (2...Nxe5 fxe5 if applicable, shutting the weak square down is still ok)
3) Breaking early is easier than when white is well prepared for it. Also you need enough pieces on the board if you ever hope to accomplish an e5 break. If you can never do that, make sure you can hold the endgame. The king on f7 sometimes has to hold it I think.
4) 1...f6 2.whatever??? fxe5 3.fxe5 accomplishes virtually nothing, other than rid black of the f7 pawn. White still has a space advantage with the e5 pawn while there is complete symmetry. In the diagram d4 is already weak. Do you also want to make black pawn e6 weak, is the question.
Conclusion: It is difficult, but the key is to put some actual pressure on the white centre. You need to decide if it is d4 that is the target, or e5. Which pawn can I isolate? You simply need to build up behind your own pawns before you decide on cxd4 or f6. After all the play on the c-file (rather than attack on the centre pawns) may be enough in which case you don't need the f6 break. Hopefully white cannot cover both sides of the board and prevent all plans.
As a caro-kann player as black and an e4 player as white, I feel that I need to understand this. When this (or a similar) pawn strcuture shows up...
When is it a good idea for black to play ...f6? Are there any general rules for this, or do you just have to "calculate?" I've been burned by the backwards e-pawn a few times playing it on the black side, but it sometimes is an annoying pawn break when I have the white pieces! Any advice? Thanks!