The two big things you really want are c.LK > c.LK xx super, and linking overheads (both UOH and f.HK) into super. The first one of these is fairly simple and just takes a bit of practice. f.HK - super only combos if it hits a crouching opponent (iirc, I might be wrong on this), and UOH into super requires you to hit at a far spacing (a spacing you can easily set up if they block c.LK > c.LK actually).
There are a couple of other useful confirms (s.MP / c.MP xx ducking xx super, f.MK - super) that might be useful, and he has a plethora of optimized juggles if you want to spend time in the lab, but I suggest starting with comboing lows and overheads into super. Being able to blow people up with damaging high-low-mixups is one of Dudleys main strengths, so you want to be able to capitalize in those situations.