I have a machine with Ubuntu 12.04 and have installed Jenkins ver. 1.424.6 using apt-get based on *this guide*, but there is a new version:
New version of Jenkins (1.447.2) is available for download (changelog).
If I press download, I get a jenkins.war file... but how do I use that for upgrading my current installation? or is that not possible before the apt repositories gets updated?
You can overwrite the existing jenkins.war file with the new one and then restart Jenkins.
This file is usually located in /usr/share/jenkins.
If this is not the case for your system, in Manage Jenkins -> System Information, it will display the path to the .war file under executable-war.