Not that complicated in a veneer brick home. But lots of work. Brick is knocked off, replaced by stone. The masons should install a new rainscreen, too--typically 15-30 lb. felt.

Because of the cost, it makes economic sense only in higher value homes, usually in conjunction with other changes. See the link below for an excellent example. Depending on the location, the makeover below is a $1-$1.3million+ home.

Here is a link that might be useful: Brick to Stone

Are you talking about the entire house - ground to roof - being brick, or a 1950's ranch with brick 4ft up? The scale is going to make a big difference in cost and options. Obviously, the bigger and higher you go, the most complicated and costly and change is going to be. Also, are you thinking of using an engineered stone veneer or natural, whole stone?