the answer isn't necessarily quick (although it can be) but is pretty easy.
1) It will attach better to more porous materials. Porous rocks (holey rock) and wood are you friend, slate and granite are not.
2) Higher light+more ferts+steady carbon source= more rapid photosynthesis; it will grow and "attach" to things faster.
If you don't have these things, that's not bad... it just means it's going to be happening slower.
In one of my low tech tanks, I started some moss a month or 2 ago and it is barely 1.5 times it's original size and hasn't safely adhered yet. Moss isn't known to shoot up like a weed (in most cases at least). Can't tell you how much longer to way, you will just have to test it.
If you are tired of seeing the medium you used to attach the moss, replace it with some microfilament line. When I use this stuff, I just leave it on forever seeing as you can hardly see it to begin with and when the moss grows it becomes practically invisible.
Probably not quite the quick and easy you were hoping for, but hope it helped!