The first step is to look at the puncture(s). The appearance and location will assist you more than anything else in determining the problem. Given only your description so far my guess is that a foreign object such as a small piece of glass, wire etc. is still in your tire and going over an obstacle drives it back into the tube or a pinch flat from low pressure. So when you remove the tube immediately place it back on the tire in the same orientation as when installed and carefully inspect the tire (or rim/tape area if the puncture is not in the exposed part of the tire) for the cause.

(Sorry - somehow the other posts did not show up, so this is a bit out of date)