Each player throws 3 darts. Player throws first for the 1 (it's the first inning, get it?). A single counts as 1, double 2, triple 3. Missed darts don't count. The opponent then throws for the 1. Second turn for the 2, etc., up to 9.
Optional rule used in Newfoundland: if you miss the 7, your score goes back to zero. If playing on to 20 (instead of 9) then the 14th inning is also a "must-score" inning.
Variant (The Yogi Berra - It ain't over till it's over - Rule) used in my house: If you score with all three of your darts, the inning stays alive, i.e., you get another three darts, until you miss one or more of them. This way you can still come back and win in the bottom of the ninth.
There is another Baseball game, which requires a dartboard with a baseball face. Never seen by the FAQ authors, we suppose that there must be special rules for these.
ADDENDUM (7-Aug-94) from Bob:
Actually, I have seen two such games. One is a cover that is pulled over the board there by creating a new board layout. It looks like a baseball diamond and outfield. There are other games that can be purchased with pull-over covers too including a "Desert Storm" version where you get to bomb Saddam Hussein's face. Yahoo! Another version I saw in June in Toronto is a top quality dartboard which is being manufactured with a baseball field screened on the face. Both these games require special rules which are supplied and have different difficulty levels for the casual or new player and the not-so-faint-of-heart.