Find some video of Buddy McGirt. He had tremendous footwork and was very skilled at getting inside. You'll see how he 'cheats' his way in, using foot feints or by subtly sliding is lead foot forward and then pulling up behind it. Also, how he uses the jab and what I refer to a a 'fencer's step'- pushing off his back foot, coming in with his jab, and then getting good position inside to avoid being hit.
Andre makes a very good point about the importance of controlling the opponent's lead hand. Trying to walk in on somebody is pretty difficult if both his hands are between you. The idea is to get past the first one and, while it is still out there, he can't throw the other one, much, so its important to move quickly.
To come in at angles, you need to first discard the idea of "side-to-side" movement, and understand that the whole game occurs in a circle, and that you create angle by controlling the turn of the circle