P.M.
My grandson (a normally happy and cooperative boy) bit a few times in daycare at about that age, so we did lots of research and asked lots of questions about this very common stage. It is usually frustration or sometimes just too much excitement (like a nipping puppy) that triggers the bite, and sometimes the discomfort of teething is also a contributing factor.
For such young children, punishment/correction after the fact is far less effective than "shadowing" the child during those situations in which he's most likely to bite.
When the tension begins to build, stick close to the little guy, and remind him gently "No biting." Give him something else to distract him, talk to him calmly to help him reset his emotions, remove him from the area, if necessary. Give him words for his feelings – upset, mad, sad – and sympathize with his frustration. You can even give him some alternative ways to act out his feelings, if that helps him deal with his very real need to "do" something.
But redirect him before he actually bites for the fastest and most peaceful resolution of the problem. My grandson and a couple of other "biters" his daycare dealt with were quickly corrected by this gentle means.
If you miss and your son bites again, please don't bite him. This does sometimes shock a child into not biting. It also sometimes reinforces the behavior and makes a child more aggressive. If he bites again, firmly but peacefully separate him from his victim and give first aid and sympathy to the bitten child. Then turn to your son and demand "NO BITE" in a stern but not angry voice. Give him something else to do.
Some moms demand an apology at that point, but I think that may simply be teaching a child to be dishonest and discount his own feelings, which create other problems later on. You should, however, model sincere apology toward the other child (and his parents). Kids learn best what they see demonstrated.
So in summary, what works best seems to be stay alert to the child's behavior, intercept before biting (works for hitting, too), give the child words to express his feelings, be firm but kind with your commands, and redirect the child's attention and energy.