mounting on exterior walls

I am assuming your talking about interior walls.  there are a few different ways to do it.  to me the best way is to get a stud finder and use painters tape to mark where your studs are then get a towel bar that matches the spacing.  there are kinds where you cut the bar to size.  this way you can use a 1" wood screw, predrill and it will be solid.  the other way is to use some sort of wall anchors and drill just deep enough to ge tthe anchor in and then screw to that.  just look at your wall thickness then choke up on the drill bit or put masking tape on it so you know to only drill untill the tape hits the wall.