"Focus Mitts - Have your partner hold one of the Mitt's head-high. Near his face. So your targeting is close to jabbing at his head. I would say begin with whichever Mitt is his lead. Now, tell him to take a shuffle-step back every time you throw the jab, timed so that he's out of punching-range. Watch the magic. All of a sudden you won't be able to touch him and it'll piss you off. But you have to practice. You have to train to step quicker. When you can finally hit the Mitt, have him take bigger steps back. When you're finally fast-enough that he can't back away and make you miss on a straight line, have him side-step to either side. You have to learn to fire your jab at angles, too. Straight-jabbing becomes too predictable.
Now here's where it gets fun. When you have this down where you can chase him down (if the guy gets too slow switch to faster guys in your class, but a good partner will get faster right along with you), tell him to counter you. Everytime you step in for that jab tell him to throw a counter-hook to the body or the head with his opposite hand. So that every time you land the jab, bing, you get popped. Sucks huh? Well there's a way to stop it. Use your opposite hand/arm to block. Don't parry, just put the limb in the way (for now). This will do WONDERS for your confidence in not worrying about being countered when you step in. Yes kids, it's JUST THAT EASY. Not really because this is a pain in the ass to practice a lot. And getting countered is very frustrating. But you'll get better as time goes on. Faster and more accurate.
Now, here's a little twist to do as well. Switch your target hands of your partner. Have him hold his REAR hand face-high and make that your target. This will suck balls because it's SOOOOO far away. At first you'll feel like you'll never hit it without being exposed. But like I say, you'll get faster at it. But then do as the previous exercise. Have him counter you with the LEAD hand. So you fire a jab at the rear pad, and he counters with a lead-hand hook to your face. His counter is going to be naturally faster because there's a lot less distance involved. Plus you won't have time to bring your rear-hand around to block. This is where keeping your chin tucked and knowing how to duck and feint will come in handy. Plus it will make you more aware of whether or not you're properly balanced when throwing the jab.
After a while you can incorporate other punches, tying combinations together and varying the counters. You'll get much more slick and better with footwork and balance, and your confidence at moving in with punches will be a lot moreso. Increase the pace as you get better as well, after a while you should be able to do this at full speed, with your eyes closed."