Poker strategy splits neatly into two parts. First of all, you need to know what your hand is worth. There is no point in playing very weak hands except for a bluff. Secondly, you need to know how to vary your game to take into account the actions of the other players.
This article assumes that you are playing in a reasonable size game, against for example nine opponents. If you are playing fewer people, you will need to adapt your strategy.
Valuing your Hand
In most poker games, you should immediately fold about two thirds of the hands you are dealt! If you are playing against nine other people, you can only expect to have the best hand one time in ten, so you want to be selective. At the same time, you don't really know what your hand is until the last card has been dealt. This means that you do need to play more than a tenth of your hands. Essentially you are looking to play hands that have a realistic chance of improvement.
Suppose you are sitting at a Hold 'em table, and you have been dealt Q7. This is the kind of hand many people are tempted to play, but you really shouldn't. The most likely improvement is to a pair of queens or a pair of sevens. A pair of sevens is unlikely to be a winning hand in Hold 'em. A pair of queens could be, but you could easily lose to someone who has a queen with a higher second card.
Now imagine you have been dealt KQ. This hand has two chances of improving to a good pair, not just one. You will also feel fairly confident about your second card, although it could be beaten if someone has an ace. A good second card (a "kicker") helps you in two ways. Firstly you are able to bet more money because you can have more confidence. Secondly if it does come to a showdown, you are of course more likely to win the pot.
In Hold 'em, hands where both cards are ten or better are usually playable. These can improve to big pairs. You can also play hands which might improve in other ways. Small pairs can improve to trips, cards of the same suit can improve to flushes, and cards with similar ranks can improve to straights.
It is with these other improvements that things get more difficult. Pairs only improve to trips one time in eight (approximately) so are they worth playing? There is no simple answer to this. It depends how much it will cost you to see the flop, and how much money you think is likely to be in the pot at the end.
Two cards of the same suit will give a flush on the flop about one time in a hundred. By the time the remaining two cards have been dealt, the odds have improved to nearly one time in ten. Continuing to call until the end of the hand is likely to be expensive, though, and it is not uncommon to find that someone has a better flush. For this reason, people sometimes play suited aces but are reluctant to play other suited pairs. A suited ace can improve to a pair of aces, or to the top flush.
Two cards of adjacent rank improve to a straight with odds slightly better than one time in a hundred. Many of the same considerations therefore apply to straights as to flushes. There is, however, no equivalent of the suited ace. You will play large connected cards (eg QK) anyway. It is not really worth playing small connected cards like 78 on the off chance of a straight.
What about 78 suited? That could improve to a straight or a flush (or a straight flush, if you are very lucky). The odds are not good, however. If you think you will be able to see the flop cheaply, and there would be a lot of money in the pot should you win, it could be worth it. However, it is a very marginal hand.
Play after the Flop
If your hand fails to improve, throw it away. A common mistake by beginners (and people who should know better) is to keep calling in the hope that the hand improves. The other temptation is to try a bluff, even when it has no realistic prospect of success.
The exception to this rule occurs when you get two of the three cards you need, so perhaps you now have four hearts. If you stay for the turn, you have about a one in five chance of hitting your flush. If you stay for turn and river, the chances are about one in three. These odds are good enough to make money in a lot of games.
The opposite of this situation occurs when you hit a high pair. It is possible that someone is hoping to complete a flush or straight. There is also the chance that you could be derailed in other less likely ways, such as someone's lower pair turning into trips. To help guard against this, you should normally bet heavily at this point. Someone with four cards to a flush may well drop out because (depending on the number of other players trying for the pot) the odds on new bets are probably unfavourable.
This situation, with some players wanting to call and others to bet, is very characteristic of Hold 'em.
Relating to Other Players
We have covered the value of your own cards, now let's think about what the other players are doing. If you are playing face to face, you may pick up clues ("tells") from players' demeanour. However, by far the most important clue is the amount of money the players are betting. This means that reading opponents is still important for the online game, where you can't see the other players.
The first question you should ask is whether the table is "loose" or "tight". A loose table is one where players are very willing to invest money in the pot, often by calling when there is no good prospect of winning. A tight table is the opposite; players drop out readily if others bet, and are selective about the cards they play.
In a sense, you should try to be the opposite of everyone else. Loose tables are very frustrating to play at. Lots of people stay in each hand until the showdown. This means that you can often lose in spite of holding good cards, because someone randomly improves a bad hand right at the end. To counter this, you need to tighten up yourself, and only play the very best hands. This is boring because you will fold even more of your hands than usual, but it is the only way to beat a loose table.
Tight tables allow for more imaginative play. If people are willing to drop out when you bet, you can try an occasional bluff. This serves two purposes. Obviously if your bluff succeeds, you win money. However, if your bluff fails, you confuse your opponents. Now they don't know whether to call your bets or not. This helps to draw extra money into the pot when you really do have a good hand.
As you play, you need to be conscious of the impression you are giving to other players. If you have just been caught bluffing, you look like a loose player, so tighten up for a while. On the other hand, if you win a showdown with a premium hand, you might look for opportunities to bluff, since you appear to be playing tight.
Now you have the mood of the table, try to focus on the individual players. The easiest thing is to note the players who are out of step with the table. Is there someone who really isn't very good, and makes feeble bluffs all the time? Perhaps another player always tends to call. That could be a hint that you shouldn't try a bluff against that player. (Such a player will lose more money by calling than by being bluffed.) Less common is the player who folds too readily, but it does happen. Against such a player you should bluff more often than usual.