Get the lift dialed (a coach helps a lot).
Then it is simple. . . just focus your training on snatches.
I like to work up in weight and then drop back down a fair amount to retain the explosiveness. With heavy weights, it feels like you are doing the lift slowly. When you drop back down to a lighter weight (maybe 60 or 70% of your heaviest single that day) for your final lifts of the day, you really move that weight fast and explosively. It helps keep the lift dialed.
As far as squats. . . as long as you do some balance work once in a while so you can catch a snatch at full squat without knocking yourself down, back squats are sufficient for strength training. You aren't going to be able to hold the bar long enough in a front squat with the weight and reps you need to really work the legs. Front squats are more for doing quick heavy singles for training the clean, IMO.
I noticed that deadlifts didn't do anything for me. As my olympic lifts got heavier, my deadlifting ability got better. . . but training deadlifts didn't help the olympic lifts.
If you use gloves or straps to do any lifting, stop using them immediately. Your grip absolutely needs to be on par with everything else in the chain. Learn the hook grip and use it for everything.