If 6.06 provides a (meta-) package for it, see the package management application: search for "flash" or "java" and see if there are packages you can just install the regular way.
The other way is to visit Adobe's and Sun's websites and download the Flash/Java for Linux from there. Both should come with an installation script (there are instructions at their site, read them for precise help) that you're supposed to run. For example if the installer was called "install-flash-player.sh" (it can be something else too), you would first make it executable either by right-clicking on the file, selecting Permissions and there checking the box to make it executable, or by running this in command line (in the directory where the file is in):
chmod +x install-flash-player.sh
Then you would run it: either double-click on it (select "run in terminal" if asked) or in command line
The same should apply to the Java package too, though that might be a .bin file. In addition at least in the Flash plugin case you can just simply copy the flashplayer-something.so file to your browser's plugin directory and restart your browser -- this is what the "installation script" effectively does, so it's up to you how you want to do it. The installer script should work for the common browsers such as Mozilla ones.
: both of those probably come in compressed archives like .tar.gz or .tar.bz2 -- unless they're .bin files which are directly executables. If you download an archive, first extract/uncompress it. The easiest way is to right-click on the file and select the menu option to extract the package -- when you extract it, you should get a directory that contains the installation script/program and a README and/or INSTALL text files that help you further. They should allow you to "install" them as a regular user (= installs for that user only) or as the superuser (root, installs system-wide, for all users).