Basics
Opponents each play one color of marbles. (Some boards use pegs instead.) Marbles can move in any direction one space at a time or by jumping over an adjoining marble to an empty space behind. If there is a series of marble-space configurations, you can keep jumping over marbles to the empty space behind until you want to stop.
Learning the Game
If you want to get good at Chinese checkers, you need to play an opponent who is better than you. A computer opponent is your best bet, since you won't feel a pressure to move quickly. You need to take your time and really look at the board to see the consequences of your potential moves.
At first, you'll likely be too busy looking at your own pieces to much notice what and how your opponent is moving. Another beginner mistake is to hop a marble as far as possible, though you'll quickly learn that's often not a great move. Once you get get these kinds of beginner mistakes out of the way, you'll begin to develop a solid game, enough so that you can really observe your opponent's strategies.
Center Line
The shortest distance between two points is a line. Since Chinese checkers is a game where you are racing an opponent to a goal, the best way to move your marbles is to march them directly across the board as if there is a line drawn from your home base to the triangle you're trying to reach. Of course, the other players will try to block your advance, just as you will try to block theirs. Still, try to gravitate toward the imaginary center line as you move.
Opening Move
A new player will often wonder which piece to first play, considering that each of the four marbles in the innermost row gives you two choices and the three marbles behind those give you the same for a total of 14 different possible opening moves. It's best to move one of the two marbles sitting at the end of the innermost row. Moving them will avoid a logjam later.
In the sidewinder move, a player moves one of those end marbles in the direction that takes it away from the center of the board. When a player moves one of the end marbles toward the center of the board, she is using the cross caterpillar move. Most players move toward the center.
Move En Masse
New players commonly make the mistake of leaving men behind. The front marbles move out aggressively, the middle ones need to catch up, then one poor lone marble finds itself bringing up the rear, having to move one space at a time. It's better to move your pieces as a group or a column so that, as much as possible, you continually move rear pieces over those ahead of them. Moving your marbles as a group also makes it easier to plug jumping holes your opponents could use.
Don't Quite Move En Masse
Of course, you could leave a few behind, say, three, which can serve as a rear guard. Since you can jump over your opponents' marbles, a rear guard, used to plug holes, can make it hard for other players to advance quickly. Just don't let these marbles get too far behind.
Also do not leave a marble behind just to prevent a player from fully filling in her target triangle. Some games of Chinese checkers even have an extra rule to prevent this. Usually the rule says that the triangle is considered filled if removing an opponent's marble would allow the would-be winner to complete the target triangle.
Endgame
Once you start putting marbles into the target triangle, take the time to fill in the perimeter first. This will avoid a logjam that forces you to move one marble at a time.