There are three steps for upgrading the software on your LON-CAPA server.

Upgrading LON-CAPA files

Download the most current loncapa-current.tar.gz.

wget http://install.lon-capa.org/versions/loncapa-current.tar.gz
tar xzvf loncapa-current.tar.gz
cd loncapa

The UPDATE command will refresh your filesystem with all the latest LON-CAPA software.

./UPDATE

Checking your Linux packages

Checking RPMs (RedHat, CentOS, Scientific Linux, SLES, openSuSE, Fedora) or debs (Ubuntu LTS, Debian)

The /usr/local/loncapa/bin/CHECKRPMS command will check that packages (rpms or debs, as appropriate for your distro) are up to date, by checking with the appropriate package repository.
/usr/local/loncapa/bin/CHECKRPMS