I can never seem to mill a surface correctly without a lot of trial and error. I pick the surface to machine, then choose the "check surfaces" and select them all. But the tool still goes all the way around the part instead of just cutting the surface that I chose, or I machine a lot of air.
I need an explanation on how to do this correctly.

Try not selecting any check surfaces, selecting them causes featurecam to use them for calculations. Generally, I only select a check surface if the tool is gouging that surface.

If I run into issues with the tool cutting stuff I don't want, I draw a containment curve to keep the tool where I want it. Then in the surface feature, in the stock tab, I select "Select curves for boundaries" and pick the curve.

Something to keep in mind with boundaries is that the curve must be drawn at or above the highest point on the surface you are cutting.

Hope that helps.

Also you might try selecting under the EDGES tab, "Don't roll over the edge at all" box and that helps to constrain the tp to that surface(s) only as well.