Download the latest version from GSL. Untar the archive by
$ tar xvf gsl-latest.tar
$ cd gsl-[version#]/
Configure the installation by
$ ./configure --prefix=/home/usrname/local
replacing the argument of the "--prefix" with the target directory for the library where you have write access. If you omit "--prefix", the installation will default to /usr/local.
Compile and install by
$ make install