Because Ubuntu tries not to distribute nonfree software with the free CD, you have to do a few things to add a flash player. There are two methods:
the "pure" method (install only flashplugin-nonfree):
1. Use your mouse to go to the top of the screen and open System -> Administration -> Software Sources
2. Enter your admin password
3. On the Ubuntu Software (Downloadable from the Internet) screen, select the buttons for universe and multiverse and Close the screen.
4. Open a terminal. Applications -> Accessories -> Terminal.
5. Type this stuff (without quotes!):
"sudo apt-get update" (enter) (supply password)
"sudo apt-get install flashplugin-nonfree"
"sudo apt-get install flashplayer-mozilla"
6. Close the terminal ("exit") and restart firefox.
The "other" method: Automatix (some people complain, but it does tend to work!)
1. Go to this site: http://www.getautomatix.com/wiki/index.php?title=Installation
2. If you are using a regular 32 bit computer, look for "Ubuntu 7.10 (Gutsy i386)", otherwise, look for your architecture and download the installer.
3. Open the installer and follow the instructions.
4. After install, go to Applications -> System Tools -> Automatix
5. Under "Codecs and Plugins", choose the flash player.
6. Click "Start" and let it finish.
You can use Automatix to install a lot of neat software, but the last time I checked, some Ubuntu purists complained that it could damage/break your installation (this is not likely to occur).