I confess, I stand 6'3", so it's not often I have this problem (though I did have a 6'4" student for a while). However, I get asked this question a lot so I'll give you my take on the issue.
As a smaller fighter, you are at a disadvantage, obviously, when you are closing on a taller figher, since as soon as you break the measure (the "safe distance" at which you can't be hit), your opponent can usually take you out with straight punches before you can land. The keys to getting inside are head movement, broken rhythm, and counter punching. You want to wait until the taller fighter fires on you, slip his strike, and push-shuffle in to a range at which you can strike. I encourage shorter fighters to immediately counter a taller fighter's jab by slipping to the outside and throwing a hard jab to the body (assuming you are in the same lead). Typically, only after you have landed the body (or groin) shot will you move upstairs to hit the head.
Head movement consists of two types: (1) a "long rhythm": at long range, keep your head moving slightly from side to side in an unpredictable manner (like a kali stick); (2) a "short rhythm": at short range, your head movement will become more exaggerated. This can be offensive, where you slip your head off to the sides with every strike you throw, or defensive, where you slip, duck, bob and weave, or snap back to avoid incoming fire. There should never be a time when your head is still, and the closer you are to your opponent, the more it should move (until, of course, you hit a clinch; you can stop moving it then

).
To drill this, have a taller partner wear boxing gloves and step in with a moderate-speed jab to your head (assume you are both in a left lead). As the jab comes, parry-check it with your right hand as you push-shuffle in, level change, and jab him in the body. Follow up with a right hook or overhand to the head (which your partner can block with a salute or cover for safety). Do the same on the other side with the cross. Make sure after your combo that you angle out to the side to which you slipped, usually with a push to the shoulder to check his near hand (in other words: don't step straight back!). You can do a similar drill using a bob and weave against hooks. A student of mine, Burrelle, is about 10 inches shorter than me and is really good at using this to get inside my punches. Once inside, it is hard for me to counter strike effectively against him, so I either have to clinch or angle out to a longer range.
In any case, your mantra should be this is: let him lead, make him miss, close the distance, and make him pay (starting downstairs first)!
Hope this helps. There are many other good drills like these that help to solve this problem, but this is as good a place as any to start.
Temet nosce,
Jim