As a skill set it is complex and requires a lot of practice. I would say the first step is to learn to read a terrain map. Learn to recognize the terrain on the ground and find your location on the map. The more dramatic the contour interval the easier the terrain association will be.
Then learn to plot coordinates and read coordinates on the map scale you plan to use. There are many different scales, so you have to pay attention to the detail.
Learn about the map itself, read the marginal data and understand it. Contour interval, scale, the declination diagram, map symbols and colors.
Learn to plot an azimuth on your map. You can go the other way and plot you desired line of march and then read the azimuth from that. However, you must learn to convert grid to magnetic, and the reverse, using the declination diagram.
Now you must know your compass. How to set a desired azimuth (some can be adjusted for declination) and then follow it. There are many difficulties to be faced when dead reckoning, such as limited visibility (low light, heavy brush, no recognizable terrain features to sight on like in a flat desert or in snow), tendencies to drift in one direction or the other, obstacles, etc. There are many techniques for overcoming these difficulties, find what works for you and practice it until it is habit.
Knowing the distance traveled is very important. Learn to do a pace count to measure distance. You can use other techniques, but I do recommend a pace count so you know when you have gone too far and need to stop and figure out what you did wrong, it happens to everyone. Handrails are a great technique, but not every situation will allow for that.
Between terrain association, pace count, and skill with a compass, you should be able to navigate by dead reckoning reasonably well. Always double check all of your steps, such as obtaining your azimuth, and setting you declination. It is easy to miss something, especially in bad weather, when you are tired, or in a hurry. Any stress can make you miss a step and end up a long way from where you want to be.
Tom L has some good insight, but a forum is a poor substitute for training and practice. There are some very good books on the subject, and the major compass manufacturers do make very good training kits. I have one from Silva and one from Brunton. They have some great learning material and even videos on line.
For practice you may consider joining a club for orienteering, if such things still exist. You can find some experienced people, have some fun, and learn valuable skills. People in such clubs are usually very helpful and friendly, not to mention enthusiastic about the subject.
If you need help finding the books, let me know. I can dig some up that I have used for teaching in the past.
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