The Board and Pieces 
The board is the shape of a six point star, with holes for possible moves of the pieces, typically marbles or pegs. The center of the board forms a hexagon with five holes along each side. Each point forms a triangle with ten (10) holes in four rows; 1 + 2 + 3 + 4 = 10. The points are typically different colors, corresponding to the colors of the pieces.
The Object 
The object of the game is to be the first to get all of your pieces from the point in front of you across the board, and completely into the point on the opposite side.
2, 3, 4, or 6 players can play a game. Each player chooses the color of his or her pieces and fills one of the points of the star with his or her pieces as follows: Two (2) players begin at the opposite ends of the star, across from each other. Three (3) players set up occupying every other point. Four (4) players set up with two on one side, across from the other two players.
Players typically agree on the method to determine who plays first, and second. (The roll of a die, coin tosses, youngest, etc.) Play usually follows a clockwise or counter-clockwise order.
On a player's turn they must move only one piece. The move may consist of moving one piece into the adjacent empty hole, the piece may jump over one adjacent piece into a empty hole, or can make two or more multiple jumps. The player can jump over their own pieces, or over the pieces of any of the other players. Each jump in a string of multiple jumps must jump only one adjacent piece landing in an empty hole. A piece cannot jump over two or more pieces in a line, but a piece can jump zig-zag over two or more pieces.
Except for the holes along the edges, all (other) holes have six holes around them, corresponding to the direction of the next move or jump.
Opening Moves 
Knowledge of openings is very important to playing Chinese Checkers well -- similar to chess. In play among experienced players there are only a few openings that are commonly seen. Although there are 14 possible first moves (7 if you eliminate symmetrical moves for the first player), experienced players play only two.
By far the most common first move is to move one of the two marbles on either end of front row of the four forward marbles one space forward and towards the center (as illustrated by green in the picture). This is the first move of the two most common openings the "sidewinder" and "cross caterpillar", there are many other less common openings.
A much less common first move sometimes played by advanced players is to move one of the marbles in the front row one space forward and away from the centerline (the red marbles in the picture nearby show these moves). This first move leads into "Squad's opening" and other similar openings.
General hints 
Get as far as possible 
One of the most basic strategies of the game is, of course, to get as far as possible. However, during play, it is not always the best move to go to the very end of a jump; sometimes you have to block your opponent. Although they may not like this, it is a real advantage to block them. Of course if you imagine a computer player, they will do this automatically if they think one extra move ahead!
Keep moves near a center line 
If you split up your pieces at the wrong moment you'll find that you will be left with a lonesome piece that will take you a lot of wasted moves to get to the end. Also, there are always more pieces in the center line than near the edges. So keeping your pieces near the center line is an important advantage as you can always move your pieces.
Get into the goal area 
If you have your pieces inside the goal area, it is also easier to feed following pieces in. The two outer edges seem to be more of an advantage. Often you may shuffle the pieces inside the goal to get more in, but don't overdo it; you have to get the external pieces in the shortest number of moves.
The piece furthest away from goal 
This is a major help in play. You should always check your last piece because it can quite rapidly become stranded and you will lose the game. Basically, before making a move always check if you can get the last piece up.