My wife and I are just starting to ride, but her hand falls asleep after riding to an extended time. Any ideas? Do we need to adjust the handlebars up/down?

The short answer - install bar ends. Bar ends allow to change your hand positions on the handlebar, I am changing mine often to avoid numness of my fingers.

My recommendation: Cane Creek Ergo Control II Bar Ends - I am using them for two years on all of my bikes. Buy two sets: for your wife and for yourself - easy to install, the must for longer rides.

Bend your elbows, and make sure your bikes fit you properly.

Check riding position. numb hands is a sign of a nerve pinch somewhere.

My guess is either the handlebars need to go up, the bend of the bars may be wrong, or she's got the "newbie death grip" going on.

Newbie death grip: every rider has this...it's when they first start riding, and grip the bars way more firmly than needed...this compresses the tissue in the palm of the hands, and makes it far more likely for numbeness, etc. Grip should be enough to keep good control, but not tight.

Are you using flat bars (MT bike style) or Drop bars (road style). If you have a flat bar HooKooEKoo has graet advice get bar ends. If you have the drop bars make sure you are moving the hands around on the bar. Do you guys ride with gloves, if not look into getting a pair.

Check that her saddle isn't angled too far down in the front, that'll cause her to slide forward, which means she'll be supporting more weight on her arms than her butt.