It seems like there are a few answers that kind-of, sort-of make sense, but that I don't know how to carry out. And I haven't found a comprehensive answer.
The First Problem
Google Test should not be an installed library, it should be built with the project. (See the FAQ.) As far as I can tell, this means the Google Test libraries are a dependency of my unit tests, and should be built when I run "make check" within my project for the first time. This should build Google Test libraries in some directory. I don't know how to do this. It mentions some autotools script that's deprecated, and I'm not sure what they're talking about or how to point my build at it properly.
The Second Problem
Assuming the build is successful, how do I write a test that uses my locally-compiled version of Google Test to run tests? I assume that there are a bunch of Makefile.am commands I put in my tests directory. But what are they? And what's an example of a unit test that uses Google Test?