There are different YAG  lasers so it really depends on which it is.  Most of the YAG lasers in use now are designed for hair removal and not particularly good for brown spots (lentigines) on the face, hands, legs, etc.   The older Q-switched YAG laser which is a green, 532 nm wavelength is a great laser for removing brown spots.

The newer, more powerful IPLs (like the Lumenis One) which have a squared off pulse width and plenty of power  (okay  I know this is getting a little technical!) are also excellent.  Some of the older models and salon models just don't have enough power or ability to customize to make them worth doing.

Please be sure you've seen a dermatologist and are sure that these brown spots are lentigines and not skin cancers or melasma.  Laser treatment of the wrong thing can be a disaster!