Dexterity was never an issue personally. Hand strength on the other hand (no pun intended) was. Advice I was given was doing some light weight training with free weights to improve grip and hand strength. What I more actively did was not push myself. I found that giving myself short breaks to stretch and relax my hands helped the most. Over time, simply operating more and more, I developed more stamina and strength. If I ignored the tightness or pain I would pay the price and develop cramps.
Another thing to consider is technique, when using a hand piece or an instrument like an elevator or curette, have a faculty member evaluate how you're employing and holding them. This may require multiple events of evaluation, you can't expect to handle these instruments well after one mentoring.
Finally, gloves. Are your gloves too small? You may want to experiment with different size gloves before sticking to one. Remember that standard exam gloves and sterile gloves are sized differently, and the same goes with brands.
Best of luck!
I had never considered this, but I believe there might be some truth here as I was of the generation just transitioning to typing being more the norm than writing, and did in fact feel I had hand issues during dental school.