What precautions should I take when flying over a mountain?
When flying over mountains Pilots will have to encounter unpredictable winds, high density altitude, steeply rising terrain and box canyons, mountain waves, rotor clouds, turbulence, and clouds covering high ground . 

http://www.swaviator.com/html/issueAS99/basics.html

It is therefore essential to take the below mentioned factors into consideration :

(1) ROUTE PLANNING : When flying over mountains Route Planning is extremely important because a straight line between two points may not always be the best way to go . Therefore, pick a route that avoids the rugged areas and highest peaks where an emergency landing could not be made. It usually takes very little extra time to bypass the most mountainous areas and follow major roads through more populated areas and lower terrain .

Do not approach a ridge until you have sufficient altitude to cross with a safety margin. If you encounter too much sink, you must have enough altitude to turn away towards lower terrain. To make that turn as easy as possible, its wise to turn your aircraft to a 45-degree angle to the ridge before you cross .

http://www.avweb.com/news/airman/190015-1.html?redirected=1

(2) THE TERRAIN FACTOR : The rising terrain will often out climb non-turbocharged aircraft. If your aircraft has a service ceiling of 14,500 ft., that is based on standard atmospheric temperature which is 59 °F at sea level and decreases an average of 3.5 °F per thousand feet. If the surface temperature at 5000 ft. is 100 degrees, the density altitude on the ground is about 9,000 ft. When you climb to an indicated altitude of 9,500 feet you have reached the service ceiling of you aircraft.

(3) THE WIND FACTOR : In a light aircraft, it is best to stay on the ground if the winds are greater than 35 miles per hour. Due to the venturi effect, winds will be much greater in the vicinity of mountain passes. Cross passes as high as possible, as downdrafts up to 2,000 feet per minute can occur on the leeward side.When strong winds of 40 to 50 miles per hour are blowing perpendicular to a mountain range, expect mountain waves and strong downdrafts for many miles on the leeward side.

(4) THE CLOUD FACTOR : The combination of rising ground and lowering ceiling can be deadly. Mountains disappear not only in clouds, but also at night. You should not fly over high territory after sunset unless you are at the minimum en route IFR altitude which provides a 2,000 ft. clearance along airways. When flying after dark, closely monitor your altitude and when in a turn, your rate of descent.

A mountain checkout flight is all that is required to get started. The checkout will enable you to operate around some pretty impressive terrain :

Flatlander Focus : Two good books on the market are The Mountain Flying Bible by Sparky Imeson, and Flying the Mountains: A Training Manual for Flying Single-Engine Aircraft by Fletcher Fairchild Anderson. Reading either one will give you a solid foundation on which to build your skills.

Most Importantly - Know Your Aircraft &amp; Its Limitations 

http://www.caa.govt.nz/safety_info/GAPs/Mountain_Flying.pdf

(a) What distance over the ground does your 
aircraft cover in a rate-one turn? 

(b) What’s the distance for a steep turn? 

(c) What speed and configuration do you use for reduced 
visibility and for a minimum radius turn? 

(d) What is the best-angle-of-climb speed? 

(e) Do you know the manoeuvring speed (VA) and 
understand its application in potentially 
turbulent conditions? 

(f) How is your aircraft performance and handling affected by 
altitude and turbulence? 

(g) How is performance affected when operating at 
maximum-all-up-weight?

Needless to say recent practice and currency are vitally important.