I compiled and installed a program from a tarball ala
make install but now I want to know where those files were installed. How can I do this?
There's no universally reliable way to do this after the fact, AFAIK. One thing that might work, if the Makefile has an uninstall target or such, would be to examine that and see what it removes; that might show you where the install put stuff.
However, the issue of keeping track of installed files has been around for a very long time, and the answer is generally package managers. What most of them do (basically) is install the package into an isolated location and then pack up the resulting files into a "package". Once that's been done, you can see what files are installed by looking inside the package (or asking the package manager).
One thing you could do would be to simulate what a package manager would do. Create a directory and install the program in it (if your program uses