Bishops in the middle game
In an attack, bishops of opposite colors tend to favor the attacker. This is because the defending opposite color bishop cannot block the attacking bishop.
Bishops in the end game
When there are fewer pieces remaining and each player has only one bishop -- each of the opposite color -- games tend to draw. This is not to say though that the game must end in a draw. The knowledge of this tendency is only useful for the player seeking to draw a game.
One bit of advice, just because you've reached an end game with opposite color bishops, don't accept a draw until you are sure it really is a draw. This generalization of opposite colored bishops leading to draws should not be taken as they must end in draws. Always fight.
Good and bad bishops
Some bishops are more useful than others. In most games, you will have one good bishop and one bad bishop. It is important to realize what makes a bishop good or bad, so as you avoid trading your good bishop for your opponent's bad bishop when possible. When you have only one bishop, there is wisdom in making it as good as possible.
A good bishop is one that is not obstructed by your own pawns. This makes the bishop active or, in other words, more mobile and attacking more squares.
The term "bad" is dangerous, because it might be implied that the bishop is not useful at all. This is not true. It is simply not as flexible as the good bishop. A bad bishop is most effective outside of your pawn chains. This way, it can attack rather than passively defend pawns.
Bishops against knights
If a knight is on the edge of the board, a bishop on the opposite color square can attack every square available to the knight. Even when the knight isn't on the edge of the board, attacking two or four of the possible squares a knight can land on can dramatically restrict a knight.
In the end game, a bishop is stronger than a knight if the pawns aren't all on one half of the board. Bishops can move from one side to the other in a single move, where a knight has to hop slowly around. However, as a lone bishop is restricted to a single color of square -- which gives the knight the advantage when the remaining pawns on the board are all near each other. Most of the time, a pair of bishops is worth as much as an extra pawn in the end game compared to a pair of knights -- as the bishops are both more mobile and will cover all of the squares.
A skewer is an attack on two lined up pieces -- where the more valuable piece is directly under attack and will be forced to move out of the way.
A bishop can deliver the most powerful skewer against against a king, rook, or queen. As queens and rooks are more valuable pieces, which also means there are far fewer situations a skewer can be effectively delivered.
As an example, consider a queen skewering a king. If the king moves out of the line of attack but still guards the revealed piece, the only reasonable exchange for the queen will usually be another queen.
In another example, a rook in a similar situation, will often find the only valuable skewers it can deliver are to gain a queen. There are of course exceptions -- but in the context of bishops, this just demonstrates how powerful bishop skewers are -- as they will make an even exchange or better.
A pin is similar to a skewer where two pieces are lined up, but the less valuable piece is in front. While bishops aren't alone in their ability to pin pieces, the fact that they are worth less than rooks and queens, means that a pinned rook or queen will likely lead to a gain in material even if the opponent attempts to unpin them.
This blog post is geared toward new players. Not that I am qualified to give advice -- I myself am not an advanced player. I merely hope to help struggling beginners.