There are a few ways to play bean bags. There is the traditional game to 21, a frame game, and a few other ways to play bean bags. Bean bags allows players to come up with creative ways to keep the game interesting, so come up with your own ideas too!
The most common game is played to 21 points. 3 points for in the hole, and 1 point for on the board. Opposing team's points cancel out, play straight to 21 or win by 2, etc. Almost everyone knows how to play this way, so I'm not going to get into the details. Check out my website to see the general rules for this game: http://beanbaginfo.webs.com/rules.htm or look at the ACO's professional standards here: http://americancornhole.org/cornhole-rules.shtml
A frame game is a newer concept brought about by the American Cornhole Organization. It is used to test the skill of a player and rank them among players across the nation. At the same time, this concept can be used in competition where players can throw a frame game heads up. It is really not recommended for backyard play against your friends, but it is a good approach to becoming a better player and keeping track of your progress. Here is the way it works.
A frame game consists of a single player throwing a series of 13 frames. The player throws 4 bags per frame, adding up the total points scored in each frame. After one frame is completed, the player walks down to the other board and throws the next frame from that side. The player must walk directly down to the other side (if he/she throws from the right side of the board at one end, he/she must throw from the left side of the board at the other end). After 13 frames are completed, the player adds up the total points from each frame. The goal is to score as many points as possible throughout the 13 frames, the maximum being 156. Compare your score to your friend's or to players across the nation by looking at the player rankings at www.americancornhole.org
Another way of playing, although it is more difficult, is to aim straight for the hole. This game is also a good way to practice your game. Only bags that go straight in the hole (without touching the board) count for points. There are many names for this type of shot...airmail, over-the-top, dunk, etc. You can keep score by adding up the amount of bags made each round or counting each airmail for 3 points. Of course each made bag will slightly touch the board while going into the hole, and it might be hard to tell if the bag bounced in or not. To solve this problem, the ACO has made a set of boxes made particularly for this game. Each box is made up of a hole with only a few inches of board around it, very intimidating at first glance! You can check out this product at http://www.americancornhole.com/category/Cornhole-Boards.html