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
- Avoid rapid movements, running, loud, excited talk.
- Stay in groups; keep children with adults.
Probability of risk is slight, provided your response is appropriate.
50 yards away with its ears up and attentive to you
- Hold small children; keep older children close to an adult.
- Do not turn your back.
- Look for sticks, rocks or other weapons and keep them at hand.
- Watch the cat at all times.
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;
- All of the above steps, plus place older children behind adults.
- Seek a safer location, or one above the lion, if available.
- Do not run.
- Appear larger. Raise arms, objects, or jackets above your head.
- Prepare to defend yourself.
Probability of attack is substantial.
Intensely staring, crouching and/or creeping toward you
- Take all the above actions.
- Moving slowly, position trees, boulders or other large objects between yourself and the lion.
- Do not lose sight of the lion.
- Smile! Show your teeth. (A woman attacked at Cuyamaca Rancho State Park may have saved herself by baring her teeth, growling and staring the lion down as it approached her).
- Make loud, menacing sounds, like yelling and growling.
- Throw things if the lion is close enough to hit.
- Use lethal weapons if you have them.
- Pepper spray may be effective if lion is downwind and close enough.
Probability of risk is serious if within 20 yards.
Poised to attack
- Prepare to defend yourself in close combat
- Fight back.
- Make menacing noises.
- Keep eye contact with the cat.
- Act aggressively toward the
- Use a stick to charge the lion, thrusting the stick toward its face.
- No stick? Yell loud and run toward the lion with arms high.
- Stay beyond striking distance of its paws.
Source: Link