Those things are really heavy

A black hole need not have infinite density. All you need is for a given mass to occupy a volume smaller than its Schwarzchild radius (at least in the case of a non-rotating uncharged black hole). In fact supermassive black holes, such as those found in the centers of galaxies can have densities lower than that of water.
http://en.wikipedia.org/wiki/Schwarzschild_radius
http://en.wikipedia.org/wiki/Schwarzschild_radius#Supermassive_black_hole

That's really weird

Incorrect:

"Black holes often have stars or gas orbiting around them. It is then possible to measure the mass of the black hole by measuring the speed of the orbiting material."

http://hubblesite.org/explore_astronomy/black_holes/encyc_mod3_q14.html