Some applications will allow you to specify the path to a library in the configure script. Something like ./configure --with-library=/home/me/library
Another option is to edit the Makefile to make it look for your library in your home directory, or wherever you compiled it.
You can also create a /usr environment within your own home directory, so relative it would be /home/me/usr and install things there as if it were a 'chroot' environment.
I'm sure there are more ideas, but I just woke up and that's probably where'd I'd start with something like that