Movers are all about 2 things: tracking and ambush. (Well, 3 things, because as
@DFOOSKING said, you'll need to add/subtract wind too usually.)
The tracking part is how you find out how fast the mover is going. When I've shot movers at K&M they've always put it out there and you can just input that (5mph IIRC). But, if that's unknown, then IMO the easiest way to do this is to buy/use a solver that will let you input MRADs per second (MRAD/s), Strelok Pro does this (not sure about the others). You use your reticle as a ruler, timing how long it takes for the mover/target to traverse one MRAD, hash to hash. You can use the stopwatch on your phone, or the military guys usually have words/phrases they memorize that equal certain lengths of time. The tracking part is what gives you your lead (plus/minus wind).
For the second part, you ambush the mover by getting out in front of it, and when the front edge of the target hits your lead (plus/minus wind) you pull the trigger.
The first time I'd shot movers, ever, no practice, never done it before, I went 9/10, 6 months later, the second time I'd ever shot movers, in pouring rain and with a couple of tenths of wind, I went 7/10, so it's not as hard as you might think. If you get the lead right (tracking), when the mover hits the line you're waiting on, you pull the trigger like you're supposed to, and voila... that's it.
FWIW, IDK if I would ever dial wind for this because IMO it's confusing enough already since it's out of the norm and IMO easier to remember two average holds (right/left) and then just adjust for wind on the fly. If I were to dial wind and it didn't work, I'd probably be all fucked up after the first miss lol. YMMV.
This is a good video on it: