Don't try to sneak away without letting your child know you're leaving just because he seems happy. Your preschooler will never get comfortable or really take part in the group if he's constantly checking to make sure you're still there.
The actual moment of parting is often the most difficult. Your three-year-old may cry or make a fuss no matter how much he enjoys himself after you leave. So try not to make too much of your child's tears or let the tears dissuade you from leaving. When it's time for you to go, offer your child a hug and a warm goodbye.
Before leaving, let your preschooler know exactly when you'll be back. Of course, your three-year-old probably has no concept of clock time. So ask the teacher what the class will be doing in the half hour or so before you'll pick your child up. Then tell your child, "I'll be back a little after you have your lunch" (or naptime or free playtime).
Talk to your child's preschool teacher. Ask her (or him) whether your child stops and joins in with the group after you've left. Or stand outside the door and after a minute or two, peek in through a window to see how your child is doing. In all likelihood, you'll find that within a few minutes of your departure, your preschooler has started doing what the other children are doing. If he isn't, then talk to the teacher about getting your child more involved in a project or a group activity as soon as he arrives.
If things don't improve or the partings get worse, then consider taking your child out of the group for a little while. After a couple of weeks at home with you, he may get bored (not because you're boring, but because he needs additional stimulation) and want to go back to the group.
Make a point of picking your child up early or on time, especially during the first few weeks. If your preschooler starts to look for you when you're expected and you haven't arrived yet, he may fly off into a panic. Show interest in what your child did that morning. If you in turn tell him about your day, make it sound as boring as possible. Don't let your child think he's missed anything by being away from you.