Flash installation is uually painless. If the tarball is called install_flash_player_10_linux.tar.gz, then unpack it:
$ tar -zxvf install_flash_player_10_linux.tar.gz
Among the unpacked files you will find some shell script or binary installer that you need to launch. Make sure to read any README file or the infos on the Adobe site.
Launching a script requires:
$ cd your-download-directory
$ . script.h
or if it's a binary installer
(change all names for your own case).