As a general rule, you should not begin a game you don't intend on completing. Although you're free to quit at any time, it's considered bad form to leave a game in progress. You should consider offering a draw or resigning.
If you want to save the game, let your opponent know you're going to leave the table. You may also want to arrange a time to resume the game. Then, click "Quit" on the lower-left side of the screen. You'll get a window with several options:
If you request "Quit and Cancel" or "Quit and Save," your opponent must agree.
If you "Quit and Forfeit," the game counts as a loss.
If you "Quit and Cancel," the game has no effect on your rating.
If you save a game, it will automatically resume the next time you start a game against the same player.
In single player games (Crosswords, Wordsearch, Cryptogram, Anagram, and Maze), if you select "Save Game," you're taken to a new page and asked to add the page to your Favorites (a.k.a. bookmark it) in your browser. To resume the game, select the bookmark in your browser.