When should a player decide to fold in Texas Hold'em Poker?
It's a hard question to answer, and depends on the player's style and whether the player likes to bluff, as well as the style and skill of the other players.

If I don't have decent hole cards (low cards or nothing matching) I fold. I might risk it if I'm one of the blinds, but if I'm raised I'll fold. If I have a decent starting hand I usually wait for the flop.

In my opinion you should bet based on the strength of your cards. Generally speaking, the games I've won have always been ones where I've consistently been conservative, and I find the same applies to my opponents. By conservative I mean don't bet unless you're sure the odds are in your favor.

For more on odds, read this article.