A common solution is to alternate your clamps between top and bottom:
Another solution is to clamp boards down across the panel as Drew suggested, although an even better variation on this solution is to use cauls, which start out curved but evenly distribute the pressure across the surface as they are flexed flat against both sides of the panel.
Read more about cauls: http://www.familyhandyman.com/woodworking/how-to-clamp/view-all#step2
But even if you use both of the above solutions, your panel can still bow and warp with changes in humidity, so it's important to let it acclimate first, as Matt suggested, by letting it sit for at least a week or two, assuming the lumber was already kiln-dried or adequately air-dried. If possible, let it acclimate to the environment in which it will ultimately be used--for example, if it will be in your dining room, let it acclimate inside your house.
You can also minimize movement by using quartersawn lumber and cutting out the pith. If you're stuck using the typically low-quality lumber from a home center, the best you can do may be to look at the grain direction and alternate it every other board, so one board will cup downward, the next will cup upward, the next downward, etc.