You would usually build and install it on the prefix $HOME. That means the binary would go into $HOME/bin, libraries into $HOME/lib and so on. Then you insure that these directories appear on $PATH, $LD_LIBRARY_PATH, $MAN_PATH, etc (usualy by editting your shell startup files) and it will work transparently.
Here's a recipe that will work with many programs
$ cd $HOME
$ mkdir src
$ cd src
$ wget http://host.name/path/to/program.tgz
$ tar xzfv program.tgz
$ cd program
$ ./configure --PREFIX=$HOME
$ make
$ make install
Note that unlike installing on /usr/local there is never any need for root privilege.