There are three ways to get a game on KGS. You can use all three at the same time. In addition, you can ask in the chat line.
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Click on one of the game offers. They are in heavy type, in the large upper panel of the room that you are in. The Open Games tab also has game offers.
This gives you little control over the settings of the game: you are accepting someone else's offer. You can change the settings from what the person offering the game has set, but if you do so without discussion, he is likely to refuse to play you.
It also has the disadvantage that the person making the offer may not want to play you anyway — particularly if you are unrated, or worse, unregistered.
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Click on the "Custom Game" button on the main menu bar, setting the options that you prefer, and waiting
Your game offer will be listed in bold in the large upper panel of the room window. Other people will be able to click on it and try to accept your offer. Whenever anyone does this, it will be up to you whether you let them play you.
If you are unrated, it will help if you say roughly what your strength is in the game notes. What you type in the notes section is displayed with your game offer. Here are three possible game notes.
- How about a game? Am new to go.
- ~15k. Please help me get a rank.
- Hi, I am 5 dan in Bolivian Go Association, looking for rank.
The "New Game" Window pops up when you click on the Custom Game button. Checking the Open List checkbox displays your game offer in in the Open Games tab. If the Open List checkbox is checked, more players will see your game offer, and you will get a game more quickly.
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Use KGS's "automatch" feature.
Click on "Play Go," the second item on the main menu. Automatch only sets up 19x19 matches, so if you are a beginner it is best to use one of the other ways of getting a game, and try to get a 9x9 game.
After you have clicked on "Play Go", set your automatch preferences. Select the type of opponent (human or bot, and playing strength) you want, whether you want to play a rated or a free (unrated) game, and the speed you want to play.
Once you have set your automatch preferences, click "Play Go" again, and check "Automatch". You will then see a rotating cross 
next to "Play Go" on the menu, indicating that the KGS automatcher is looking for a partner for you. Cntrl-n has the same effect as checking the automatch box.
When a partner has been found by Automatch, you will see a conspicuous count-down from 10. This indicates that the game has already started. It is now too late for you to change your mind about playing. If you leave a rated Automatch game, even before move 10, you will be marked as an escaper. So, do not select "Automatch" unless you are sure that you want to play.
Automatch gives you less control over the settings of the game than when you make a custom game of your own.
The fastest way to get a game is to use all three ways at the same time. You can also announce in the room chat that you want a game. If you are having difficulty getting a game, you can often get good suggestions to speed up the process in the room chat. Please ask and please be persistent.
