Because JDownloader isn't part of the Linux Mint Software Center, you have to download the automated Install/Start-Script from http://212.117.163.148/jd.sh.

After downloading, place the file wherever you want, best place for me is the Desktop (because that is the file, which starts JDownloader after the installation).

If you want to edit the Installation-path, open the file with a text-editor and edit line 19. Default is "~/.jd" (home).

Now you have to make the file executable. Right-click on it and select "Properties". Go to the Permissions-Tab and mark the option "Allow executing file as program". Then open the file again.

JDownloader should now start the installation.

When the installation is complete, run the file again. Now JDownloader should start.