First download the installer - here. Download and uncompress the archive. Open the console and navigate to the just created directory. Then type the following command;
./flashplayer-installer
The instaler will ask you to close all your running browsers. Close them. The next step is to select the installation folder, and install the player. By default this folder is the firefox plugins folder:/home/username/.mozilla/plugins
To get Opera use the new flash player open Opera. Select Tools -> Preferences -> Advanced -> Plug-in Options -> Change Path
Then select the directory, where you just installed the flash player, select Ok and press the Find New ... button from the Plug-ins window. Thats all :)
Enjoy your flash 9 player for linux.