When there aren't many other players in a pot
Simply put, it's easier to trick one or two people than several. With fewer hands out there, chances are better that no one has made a reasonable hand. If this is the case, a bluff can win even without other factors to help "sell" it. This is fairly common though, so many players won't believe you. Some will stay in the hand just to "keep you honest", so sometimes this needs to be a persistent bluff over a period of two or three betting rounds. That can be costly if they don't fall for it. You need to know the players before you use this routine type of bluff.
When you're up against fairly tight players
Those that tend to fold easily are the biggest targets of a bluff. Bets will be put out just as a form of information gathering on this player's hand. If you bluff early (pre-flop, flop) against a very tight player and they don't buckle, you should think twice about trying it again on a future round. They have something. Your job is to determine whether they have a made or drawing hand. Once again, you need to know the players. There is also a not uncommon type of player who is often described as "unbluffable". This is typically a newer player who still wants to play every hand to the river. Trying to bluff at one of these fellows is a huge mistake. Ironically, experienced players are easier to bluff because they have learned to make laydowns when they sense danger. But even in this case a successful bluff depends on certain types of board cards appearing (see below).
On an ugly river
If there was an obvious draw on the board but the river is a blank, it can be a good opportunity to bluff if you think your opponent was on the draw. Since his draw missed, he's probably left with a weak hand. But if your hand is also weak, a bet here could be the only way to win. Most opponents will throw away a busted draw without thinking about whether it could still be better than your hand.
You're in late position and everyone else checked
This requires some judgment of the other players' styles. It will most likely force some players out, but not all. This is a pretty common bluff, and many players will stay in just because of bet odds or again "to keep you honest". This is another example of a bluff that needs to be more persistent over a couple betting rounds. But beware making this play against someone prone to check-raising. You want to be up against tight, straightforward players who bet when they have something and check when they don't.
You raised pre-flop and missed
Of course, they don't know you missed! This is especially true when an ace flops. When you raise per-flop and then bet out when an ace hits the board, many players will think it is "obvious" that you have an ace in your hand. But this can be dangerous, and you really have to evaluate to board before you get into this one. Sometimes it's good to bluff when AK misses, sometimes when 99 misses. You have to really feel this one out.
Other players are afraid of you
A lot depends on how other players perceive you. If you just won a hand through good play, the players who said "nice hand" are the ones who now respect you. They will more likely fold to your bluff if you play it right. The trick is to play the hand exactly the same way you played the other winning hand. Give it the "here we go again" act.
When the flop is ragged
Many players will fold automatically if all they have is overcards. With a rainbow flop of 269, not many players will have much. This is another example of a bluff that works better against good players. Bad players are more likely to be playing cards like 6's and 9's, as well as more likely to call even if they don't have a pair. Once again, know your players.
When the board pairs
This is especially useful when the pair is 88 or lower, because players are less likely to have those cards in their hands. Unless they are bad players of course, in which case you really shouldn't be bluffing them anyway. If someone calls you here slow down tread carefully, they could be slow-playing a big hand.
Keep in mind that these are pretty common situations for a bluff. Many players are familiar with these, and some will call you because they recognize that you might bet without a hand. Thankfully there are players out there who will fold if they have a weak hand even if they suspect you have nothing either. These are the people you must target. Don't let yourself get carried away trying to "steal" hands; most of the time it just won't work. The main thing is always to know your players and to do it just often enough that it keeps working.
Semi-bluffing in Texas Holdem is most profitable in typical bluffing situations. Its usefulness comes from the fact that players who recognize a bluff won't necessarily recognize when you make your draw. It is more useful (and preferable) against several players, as opposed to outright bluffing, since the odds tend to be better. Other than that, you'll want to use semi-bluffing in late position, usually on the flop or turn, against ragged flops, and against poor players.
Let's say you have a Jack of Hearts and a Ten of Hearts. The pre-flop betting round concludes with six players investing two bets each. The flop is Ace of Hearts, Queen of Spades, Seven of Hearts.
You are in a middle position, and decide to semi-bluff. Why? You've got draws, that's why! Any Heart or King will give you a hand. Whenever you have multiple draws like that, start thinking of what would be ideal. If a Heart pops up you have to worry about a higher flush draw, so you probably want the King of Hearts, as he is otherwise the most likely to be in someone's hand. A Queen of Hearts would be dangerous for you, since you'd be looking at a royal flush draw vs. a potentially made full house. Ideally you want a non-Heart King. That would give you the nuts.
For simplicity's sake though, let's say that in your evaluation, either a flush or straight will give you a winning hand. You have twelve outs (don't count the King of Hearts twice). That's a little better than a 25% chance of hitting a winning card on the turn. Even re-raising or check-raising would be a good idea in this position based purely on odds. Even if you miss on the turn, you could continue to bet it right out.
When you've been caught bluffing recently
You've been labeled as a poor bluffer already. Ride it out. Let them forget that hand. Start rebuilding a reputation as a straight player so you can eventually try a bluff again later (and hopefully not screw it up again).
Against a dangerous flop
If the flop has an Ace, chances are that someone has a pair of aces. Aces tend to make it beyond pre-flop. Also, players tend to continue to play their Aces. Don't bluff against an Ace unless you raised pre-flop and you think players will give you credit for Ace-King or Ace-Queen. You also don't want to bluff against a flop like KQ9. The chances are too good that someone has something they'll stick with.
Against several players
Chances are that someone has something that they'll stick with. By bluffing in this situation, you just become an agent of that player. From an odds perspective, this is never worth it.
Against bad players
As much as they love to bluff, they also love to catch someone in a bluff. They're much more likely to "keep you honest" because they don't realize what a money-loser that is. And sometimes they actually think that bottom pair is a good hand against a board containing four cards to a straight. It's much more profitable to play straight up in these games.
You just lost a big hand or have lost a series of hands
Even if you're not on tilt, the other players will expect you to be on tilt, and will more readily call you.
You limped in, or are in a blind position
You really have to evaluate the flop, but generally other players will think you have a poor hand and suspect bluff.
They are keeping the initiative despite a poor flop
If they bet pre-flop from a poor position, and the flop is something like 4, 5, 5, they are probably just trying to keep momentum going and bluff their way out of this hand. They probably have genuinely zero drawing chances with overcards or maybe an overpair, but a re-raise could have them rethink that strategy. It might also give you a betting round or two to try and make YOUR hand.
There are only two players in the hand
It's you and them. Heads-up pots are the most common time to bluff, because it's easy to trick just one person. Use the board and your memory of previous hands to determine what they might have.
The flop doesn't have any draws
Sometimes someone will bet in this case to eliminate the ability to acquire a draw, sometimes because they have a good hand. You really have to know the player.
They bet on the Flop, then checked on the turn
If there was a draw, and it didn't hit, they are probably just buying a free card. Bet back against them and take the initiative.
They bet on the flop, bet on the turn, then checked on the river
Same as before, but they were probably semi-bluffing a hand with a several outs. Evaluate the board very carefully to see if any likely draws hit. If not, bet back at them.