Here is a pretty good explanation (there are others in web-space):
Mil_Dot_User_Guide.
You NEED four things: a good eye for estimating fractional distances between mil-dots, a good memory for the approximate height and width of several common objects, the mathematical formula shown in the guide (take care of matching units-work in yards or work in meters-don't mix) and a drop table for your particular ammunition (you can use the muzzle velocity and a ballistic program or be more empirical and actually shoot the rifle at distances from 50 yards to what every your gun and you can actually perform).
Estimate the distance by finding an object downrange near the target and recalling its size, measuring it with the reticle as 'so many dots' and apply the math formula. Use your drop table to determine a 'hold'; this can be 'applied' by twisting the elevation turret or directly on the target by holding to some number (and fraction) of dots on the reticle.
Wind estimation works partially by experience, part by guesswork and part by the same method above applied horizontally.
The difference between a mil dot scope and a scope with some other form of 'compensation markings' is one of universal versus specific. The mil-dot system is universal except for needing an ammo specific drop table. The compensation type is based on an average ammo concept-the most likely round for the caliber and game taken with that caliber. With a mil-dot precise placement of the shot is possible, with the compensation type some acceptable strike zone is the best one can do.
Most mil-dot scopes are variables. There are two different mil-dot reticle constructions. The less expensive reticle in the normal place must be set to a specific power (or an additional computation must be performed); the more expensive reticle in/on the 'front plane' enlarges or shrinks the reticle as the power is dialed up and down--i.e. no additional magnification computation.
Mil-dot scopes are more expensive because of several factors: higher power, more light gathering ability, target turrets, reticle position and other extras specific to topics like parallax and the ever present novelty cost.
I've used a mil-dot scope for many years, the math is second nature as are 'sizes'. With a well understood gun/ammo and a good drop table, I can put a shot on target about the time a second can get an accurate estimate of range with a laser range finder and speak it out loud. With a bit of practice this is something anyone can do.