There are several different ways of doing all of this. From what I've read it seems to be common to move the objects, detect a collision then solve the intersection by moving it along a vector make the objects not intersect anymore and then apply some force/impulse to make it bounce (if that's what you want, otherwise just move them apart).
The first circle to the left might be where the intersection is detected and the red vector is the direction it has been moving. Then moving it along the normal of the surface (green vector) it would appear sliding along this plane. This might be sufficient for your application.
EDIT: Just realized the image is a bit misleading. The image implies the sphere that is intersecting the plane still is moving along the red vector but my point is that it has moved along its entire vector and should only be moved "up" along the plane's normal. But the red vector is the direction it has already moved (to get to its current position). Sorry, this is perhaps quite confusing. If you have any questions about this, please ask.