Warm it up properly. That means at least five minutes doing light passes or juggling and jinking with a ball, then some sweeps and hits.
The most important thing that you should definitely do is hold the stick quite tight in your hand so that the vibrations are absorbed by your arms and body. The loser you hold a hockey stick the more it will vibrate within your hand thus possibly causing some discomfort when hitting.
Chat with our AI personalities
The bat is going to vibrate, you can't stop that (unless you get a composite bat). I assume you're complaining more about the sting you get sometimes when you hit the ball? This happens when you don't hit the ball on the sweet spot of your bat.
Also, wear batting gloves.