The key getting close and landing punches is making the other guy miss his. Jake LaMotta, his opponents said, was easy to hit with jabs, hard to hit with anything else: he'd give you the jab to get you to throw something to counter off of. Other guys will try to take away the jab, make a guy afraid to throw it because then they can walk right up on him. So I would suggest three things.
First, get real good at gauging distance. That way you can stay just out of punching range, not getting hit, and move in by slipping a jab, parrying, etc...throw your punches and get out. Watch Ruben Olivares fight tall guys and see what he does. Constant pressure without getting hit needlessly.
Second, develope top flight defensive skills. Never ever put your gloves around your head because you can't punch while he is punching your gloves. Learn to slip jabs, to parry jabs, to draw and slip right hands. And learn to counter everytime you do. That is how you get inside without eating punches and get to land clean punches of your own. In practicing this do yourself a favor: Learn the slip and the initial counter perfectly before you start trying to make the move and throw a bunch of punches. That will screw you.
Third, worry more about your feet than your hands. Messed up footwork will make it impossible for you to close distance quickly, much less to punch effectively when and while you do so.
Last, if anybody is telling you to put your gloves up and march forward, get rid of that individual. Pressing a fight, being effective and avoiding punches is an art, more so, in my opinion, than skipping around the ring and slap fighting. Learn your defense and footwork.