If the note is at the start of a bar, i.e. there are notes after it, then it is a down bow. If the note is the last of a bar, i.e. on the music sheet it will be a single note followed by the bar line.. the bar does not equal the full beat count.. then it is an up bow.
Does that make sense?.. so if the beat count is four and the first note is worth one beat followed by other notes that make up the total count of four, then it's a down bow. If the first note is worth one, but there are no other notes to make up the count, and no rests, etc, in the bar, then it's an up bow.
For example..
http://www.8notes.com/scores/2734.asp?ftype=gif
The first note to this is a down bow.
http://www.8notes.com/scores/9645.asp?ftype=gif
Ignore the slur to avoid any confusion, but the first note of this piece would be an up bow.
Does that help?