Hi Faith, down bows often fall on the strong beats of the measure, while up bows are used on weak beats. This is an oversimplification but, let’s imagine your music has 4 beats a measure. The first and third beats are strong beats. The second and fourth beats are weak beats. We don’t always have the luxury of bowing according to strong or weak beats, but that’s a rule that will help you decide.
There’s also what’s called the pick up. That is a single beat, sometimes one note that is just before the first beat of the next measure, where the music begins on a strong beat. The pick up is preferably bowed on an up bow. Pick up notes can happen any place in the music, but they usually are on a weak beat and lead to a note that falls on a ‘down beat’ or strong beat.
Slurs in the music complicate matters, and we often find the music doesn’t always fit neatly with the bowing, but we have to push through it. Like, sometimes you start out feeling like the bowing feels right, then it suddenly feels backwards for a short while, then it rights itself again. In this case, we have to observe the slurs and bowings given, but the most important thing to do is make the music sound right, and don’t just ‘play the bowing’. Usually that involves bow planning, which is a topic for another time!
If you want to show me your music in a screen cap, I can give you a quick answer for a particular piece. Sometimes it really matters if you use up bow or down bow. Other times, it matters not at all. Cheers!