They don't actually fly - they don't have wings at any stage - but many types of spider, when they are hatched, spin a thread which acts as a kind of 'balloon' so that they float away, which makes it look as if they are flying. This is beautifully described in the children's story, Charlotte's Web.
What happens is that the spiderlings climb up on to a branch or high point and point their spinnarets (the parts from which they spin their silk) in the air. The breeze seems to activate the spinnarets in some way, so that the baby spiders then produce a line of silk which soon gets long enough to be pulled away by the air currents (the way, if you let go of a kite, it wil usually get carried away by the wind). The little spiders are so light that it doesn't take much of a breeze to carry them.
You can occasionally see this happen with hundreds of baby spiders at a time. It's an amazing sight - you can see it here.