Any hard hand below the value of 12 can be hit without concern: the highest card you're likely to be dealt will be a 10 value card and this can never put you over 21 when added to a hand of less than 12. In order to decide on a hand of more than 12 whether you should hit or stand you must consider two questions: what is your total, and what is the dealer's upcard.
If the dealer shows an upcard of 7 or higher one should assume as if he will have a hand of 17 and therefore he will have to stand on it. Clearly, this isn't always the case, but it does happen a fair amount; remember that a 10, J, Q, or K, will put him at 17; that's a reasonably large percentage of the cards available. If therefore, your total is less than 17 it is worth trying to improve it, as he will end up with a 17. It is for this reason that you should hit on any hand you have of 12 through to 16 if the dealer shows A, a 10 value card, 9, 8, or 7.
If however, the dealer shows a 2,3,4,5, or 6, this is known as a bust, or stiff card, and you should always stand on it, except for if you have a hard 12 and the dealer has a 2, or 3. The logic behind this move is simple: When the dealer has a 2 or 3 as an upcard there are fewer cards that could bust your hand - The idea in this situation is to keep a valid hand for yourself whilst forcing the dealer to keep hitting and ultimately bust.
If you have a hard 17 or higher, you should always, always stand on it. It doesn't matter what the dealer is showing; the odds are stacked in favor of a bust if you hit in this situation - don't do it! Furthermore, if you have an original hand of 19 or more, the odds are stacked in your favor to win, so why take the risk.
Any simple internet search will provide you with a detailed table of basic strategy. This blackjack strategy assesses exactly what the chances of particular hands coming up are, and advices you accordingly. It does take a while to internalize basic blackjack strategy but it is well worth doing so. One way to make sure it sinks in is to play blackjack online. In an online blackjack game you can sit with you basic strategy table next to you and no one need be any the wiser; it's really the best training for getting out into the live play world.