1. Download it from here (now here). The beta has been closed and Adobe plans to release a 64-bit linux version soon. In the meanwhile you can get the latest version here (the md5 checksum is 5aa962abc2e2c85a5efee6a39a6a91a0) and cross your fingers for html5 
. (NB: The screenshot is from a previous release, however the actual binary *is* the latest. You should consider using flashblock (package xul-ext-flashblock in Debian/Ubuntu) or an other alternative (gnash) until Adobe releases a security fix.)
2. Unpackage it using a terminal (with the assumption your firefox downloads into your Desktop as default):cd Desktoplibflashplayer-10.0.32.18.linux-x86_64.so.tar.gz
tar xvzf
(The name of the tar.gz file may change when a new version is released, change accordingly).
3. Create a plugin directory in your $HOME (instead of a system directory):
cd
mkdir -p .mozilla/plugins
4. Move the file to the plugin directory:mv Desktop/libflashplayer.so .mozilla/plugins
5. Restart firefox. Go to about:plugins to see if it’s enabled:
That’s it.
Edit: Alternatively, you can use the graphical approach:
1. go to the download pages and click on “Download 64-bit Plugin for Linux (TAR.GZ, 3.64 MB)”.
2. select “Open with ” in firefox (you have to click on open to enable the ok button) and clck on OK.
3. The archive manager will open and show you the libflashplayer.so file.
4. Click on extra and a save window will open.
5. Type ctrl + h to show hidden files. Go to .mozilla (dubble click).
6. If no “plugins” directory is present, click on “Create Folder” on the top right and type as name “plugins” (without the quotes). Press Ener.
7. Click on Extract.
8. Click on Close on the windows showing the result.
9. Close the archive manager.
10. Restart firefox.