Illusions
There is a psychological aspect to mountain flying. In the initial stages, it requires a good deal of self-control, as you overcome a certain amount of fear and tension, which is not good when you really need to be relaxed on the controls. You will also have to cope with some optical illusions.
Almost the first thing you will notice is the lack of a natural horizon, and will maybe want to use the mountain tops or sides as a substitute. This, however, will probably cause a climb, or other exaggerated attitudes, and make it difficult to estimate the height of distant ground, either from a cockpit or on the ground itself, so you will find it best to superimpose a horizon of your own below the peaks. This is where using your instruments will help, both to keep attitude and give you a good idea of your height and speed (however, you’re not supposed to be instrument flying!).
Close to the ground, you will get an impression of increased speed, especially near to a ridge. For example, climbing along a long shallow slope is often coupled with an unconscious attempt to maintain height without increasing power so, unless you keep an eye on the ASI, you will be in danger of gradually reducing speed—if your airspeed is reducing, then either the nose has been lifted or you're in a downdraught (downdraughts will be associated with a loss of height or airspeed for the same power). You can also tell if you're in a downdraught by watching the position of the nose—if it yaws into the slope, the air is flowing downwards and vice versa. A lack of cloud above, i.e. descending air, is also a possible indication.

Downdraughts can frequently exceed your climbing capabilities. Strong updraughts can suspend you in mid-air with zero power – if the air subsides suddenly, you will be going down faster than you can apply it. Do not fight it, but guide the aircraft towards a lifting slope, or try for a cleaner column of air. You might get help from the ground cushion, but the effect will be less on a slope or grass. When valley flying, upslopes or slopes exposed to the sun can produce updraughts, so place yourself on a converging course to the line of the ridge and positioned to obtain a straight flight path two thirds up the slope and one across, which is generally the area of smoothest flight. However, local conditions could vary this.

You could climb on a lee slope (that is, the other side from where the wind is coming from), taking advantage of the updraught formed by stronger wind returning on itself
(i.e. riding the backlash, which tends to occur with abrupt surfaces).

Also, there is so little room to manoeuvre if something goes wrong, or you meet someone coming the other way. If you have to do this, converging on the ridge line at 45o gives you the best chance of an escape route.
Similarly, try and avoid flight along lee slopes, but if you need to (because life's sometimes like that), smoothest flight will be obtained by flying as close as possible to the ground, say about six inches, so you’re in the boundary layer, which is a steady movement of air close to the surface, with a vertical element. This gives even less room for error, though. A good illustration of the boundary layer comes from your car after it's just been washed—water left on the bodywork will not be affected by the air flowing over it, because it's in a layer all to itself. Air next to mountains behaves in the same way and, when landing at least, will be mostly what you work with.