There are many ways to do this.....
1. Rest-this is the most common.
2. Active recovery-this is where you would do some really light work for the sore muscle group. So let's say you did some heavy curls and your biceps are sore the next day. You could do some VERY light bicep work the following day just to get some blood flowing. It will help you recover.
3. There is something I read about and I don't know if it works but it sounds like it would. Taking the biceps as the example, the day after a heavy bicep workout you would do some forearm work. This would pump the forearms and that means the blood would be forced through the upper arms and in theory increase circulation in the bicep area.
4. Another active recovery thing...this one is good no matter what you trained and is sore from the previous day. Go for a walk, play some ball do something that isn't related to weight training. Besides helping with soreness it is nice to get out and do something.