Yup the difference between degrees and mils is just that it's a different system really. You'll find on less expensive compasses that the degrees are in 5 degree increments (generally) and that the more comprehensive compasses that they are in smaller increments leading to greater accuracy. Learning to hold the compass level is a very important step as an off kilter compass can throw your readings off.
Peter Cliff's book is excellent, comprehensive and easy to understand. Which a lot of books aren't.
Knowing where you are on the map is a good habit to stay in as Uilleachan says. Even if I don't have a compass out I'll periodically be checking my position to the map. With time you don't rely on the compass to do this though a periodic double check is good practice. Learning to interpret the map properly is a good thing. Whether O.S., Harveys or some other. Get to know the symbols and what's a convex or concave slope. Makes life so much easier. The likes of Memory Map have a 3D function where the graphics and shading really help here. Also when mountain travelling in winter aids as to avalanche avoidance due to weather and slope severity. (Also makes life easier as it helps you cutting out loosing height unnecessarily due to poor route selection; I'd rather walk a little further along a contour than loose height gained in mountainous terrain).
If you do go down the route of printing out maps for use in the hills make sure you don't print off too small a section. This can be disastrous in certain terrains as if you get lots somewhere where it's relatively featureless or visibility is hindered then with a wee map you may not be able to triangulate your position - (so speaks the embarrassed voice of experience
). Also on the triangulation front I carry a Silva protractor
to allow me to do so from objects far away on the map as you don't want to use a straight edge from a ferrous material like the back of a knife as it'll affect your compass needle. (Also keep radios, mobiles and magnetic jewellery away from your compass.)
Some great advice being posted up by folk, also worth a wee look here(
LINK). It's aimed at kids but is a very simple clear way to grasp the basics. Some folk teach navigation as a black art, but it doesn't need to be. Silva's 1-2-3 step guide is fantastically simple and logical.