As Granny says, the most obvious reason for hand numbness is that you are putting too much weight on your hands. Modern bicycles with their admonitions for smaller than ideal sizes and threadless headsets don't put the bars high enough for REAL(tm) people.

The rule at one time was that the bar tops weren't suppose to be more than one inch below the saddle nose. (Anyone see that on any modern bike lately?) Most modern bikes start out with 3 inches below. Consequently you are supporing far too much weight on your hands and pushing on the ulnar nerve.

You might have your local bike shop raise the bars as much as possible and check your position to determine if the reach is too long as well.

Gloves and bar tape are derigor so I won't suggest them.