The faster you move the bow, the richer the sound coming from the string will be, but make sure you get all the notes in before running out of bow hair.
As you get better, pay more attention to how you move the bow. Changing directions (up to down, etc.) is, to a large extent, equivalent to taking a breath while singing. Experiment with different bowing speed and pressure.
Sheet music will generally include bowing notation intermittently. The "up bow" mark looks like a V and the "down bow mark" like a staple or a square missing its bottom side. Up means you should start at the tip and push the bow, and down means you should start at the frog (which is where your hand is holding the bow) and pull the bow. An up-bow usually generates a softer sound, while a down-bow is stronger and more assertive. Feel free to pencil in your own marks, but remember the printed bowing marks are there for a musical reason, so they should usually be respected.
Be sure to practice using the whole length of the bow.