Watch your opponent's footwork. Try changing your own steps, then watch how they "counter" with their footwork. We used to do "hands free" takedown drills, where two guys sparred while holding relay batons with both hands behind our back (like you're wearing handcuffs). You didn't have your "hooks" to grapple with, so the only way to take a guy down was to set up his footwork and attack at the appropriate time.
Play with putting pressure on your opponent in different ways:
Feigning shots
Switching to southpaw
Switching circling direction
Changing your elevation
Bumping with your shoulder
Tapping the chin, shoulder, forehead, headgear, knees, hands, etc with your hands
Feigning hook ups (collar ties)
All of these things, and more, can affect your opponent's footwork. If you can bring the shot to you, then it's much easier to succeed with your takedown. If you can successfully learn to take guys down with no hands, then takedowns are super easy when you add your hands back into the mix.
Wrestling is a fairly simple game. Even olympic level wrestlers only typically use a select few techniques (3-4) from each position (standing, top, bottom). They may have a wider arsenal that they KNOW, but the trick to wrestling is to be HIGH LEVEL at a FEW techniques.
My personal wrestling style is offensive. I usually like to keep pressure on my opponent, whether we're tied up or not, and dictate the pace of the bout. I like to come in quickly circling "outside" to make start bringing his lead foot towards me, then quickly change directions, which usually makes him plant his lead foot. If he's slow, I'll shoot the double or single leg on the first one. If he's quick, I'll use the direction change to aggressively tie up. I'll break loose and repeat. 2nd or 3rd time, they almost ALWAYS leave their lead heel planted to brace for my tie up, giving me an easy single leg or snatch single.
Against a guy like me that puts a lot of pressure, I use evasive footwork to make him chase me. If he ties up aggressively, then I'll lower my elevation (drop one knee if I have to) and put pressure UP against his tie up to get him used to pushing forward and down, putting his weight on his toes. Then I'll break the tie up, and bait him into tying up again... When he does, I'll either arm drag/duck under, or firemans (or even standing granby).
Against a guy that makes a lot of linear shots (doubles, singles), I'll bait him with my lead leg, then stuff his shot with my rear leg hip, and slap on a front headlock or over-under tip, then roll him over to his back.
Against a guy that shoots a lot of circular shots (snatch singles, arm drags, duck unders), I'll look for the wizzers, or front 3/4 stack.
Moral of the story, have a game plan, but plan to utilize HIS game-plan against him.