Hiking on the west coast of British Columbia, there are likely to be cougars around the trails. What do you do if you see one?
I actually had a site bookmarked for this very reason that provided some good, sound advice. I've always heard that a cougar (mountain lion) generally doesn't let you see it unless its considering attacking.
100 yards away or more that is unattentive to you
Probability of risk is slight, provided your response is appropriate.
50 yards away with its ears up and attentive to you
Probability of attack is slight for adults given proper response. Probability of attack is serious for unaccompanied children.
Less than 50 yards away, staring intensely at you, or hiding;
Probability of attack is substantial.
Intensely staring, crouching and/or creeping toward you
Probability of risk is serious if within 20 yards.
Poised to attack
I think these signs in California and elsewhere describe it quite simply:
This video is quite a good instruction. :-)
This article is quite interesting, though not really useful. Read the discussion though.
But beware! This strategy might not be valid for other beasts of prey, such as lions. In this video, the man instructs to be quiet and stay low not to agitate the beast. Also, man in this video is staying low (in fact, he's almost lying) and threatening the lion with toilet paper (!) if necessary.