If you mean avoid one after it is fired at you, forget it.  Turning downward and toward the incoming missile is generally the preferred method if it is already on the way, but a large airliner cannot really maneuver quickly enough nor aggressively enought to make a difference.  If it's already been fired at you and you're in an airliner, pray.  Maybe it will misguide.  The SA-7 "Grail" (the most common missile in terrorist hands) has a fairly low PsubK (Probability of Kill), which is further reduced by the poorly trained terrorists operating it.  It is strictly a tail-chase weapon with a very narrow field of view and a low angular tracking rate, so the operator really needs to know his stuff to expect success.

It it's a Stinger, or a Bofors RBS 70, or a British Starstreak, Starburst, or Javelin, just bend over and kiss your sorry butt good bye.

If you mean avoid one before it is fired at you, there are a number of options.  If the manpad operator is not expecting you, the "as low as possible and as fast as possible" approach is generally best.  If he's sitting at the end of the runway as he sees you taxiing out and then taking off so he's fully ready for you, and he's expecting you to overfly his position, your best bet may be to level off shortly after rotating, cleaning up the aircraft and accelerating, and also turning hard either to the left or right so he never gets a view of your engines' exhaust nozzle.