Installing drivers the official way
As I said in my comment, the supported way to install hardware drivers is by running System->Administration->Additional Drivers, just as software should be installed from Applications->Software Centre.
When you install drivers from Additional Drivers, choose the recommended driver and enable it. Once you have done this, the window should look something like this:

If no drivers are shown, it probably means that you don't need to install any.
You should only install drivers from .run files if:
- You don't have an internet connection on your Ubuntu computer.
- There is no other way to install the drivers.
Installing graphics drivers from .run files
I have, in the past, been without an internet connection due to a Windows XP only modem. These are the steps I took to install my (NVidia) graphics drivers (original forum post):
- Save the .run file in your home folder. This should have the path
/home/YOURUSERNAME. You can get to this from Places->Home Folder.
- Press Ctrl+Alt+F1. This should bring up a text mode command line interface.
- Log in by first entering your user name then your password. Note that when you enter your password you will not see the letters of your password appear on the screen while you type. This is normal and is done for security reasons.
Once logged in, enter the following commands by typing them in, then pressing enter:
cd ~
sudo /etc/init.d/gdm stop
sudo chmod +x NVIDIA-Linux-x86-185.18.36-pkg1.run
sudo ./NVIDIA-Linux-x86-185.18.36-pkg1.run
Wait for the installer to finish then enter this command: sudo /etc/init.d/gdm start. This should bring back the graphical interface.
I'm not entirely sure if this step is required and, to be honest, I don't know what it does but when I installed the driver I opened a terminal Applications->Accessories->Terminal and entered this command: sudo nvidia-xconfig --add-argb-glx-visuals. This enabled me to enable visual effects.
Installing other programs from .run files
Occasionally, some applications and games (eg. some from the Humble Indie Bundle) have .run installers. Before installing using these, check to see if:
- it is available from the Software Centre
- it is available as a .deb file, which will open in the Software Centre
You can install .run files from the graphical interface, but using a terminal is more likely to give you useful feedback. To install a .run file you need to:
- make it executable.
- execute it
This is because .run files are just executable programs that do some unknown magic to install the program. This is similar to what .exe installers do on Windows and is different to the normal methods (at best, using the Software Centre, at worst using .deb files) in which applications are installed in a standard way and can be easily removed.
Graphical Method
- Right click on the file in the file manager and click 'Properties'. Click the 'Permissions' tab and tick the box that says 'Allow executing file as program'.
- Double click the file to execute it.
If this method doesn't work, try using the terminal method.
Terminal Method
Assume the file is called some-app.run and is in the folder /home/user/Downloads. You will need to modify these instructions to fit your situation.
Open a terminal (Applications->Accessories->Terminal).
enter cd /home/user/Downloads
- enter
chmod +x some-app.run
enter ./some-app.run
if step 4 fails with a message including 'permission denied', try entering sudo ./some-app.run (you will need to enter your password for this).
Notes
- Sometimes you will come across .bin files. These are basically the same as .run files.
- The method to install .run files can be used to execute any file (as long as it has some sort of executable code in it.
- Be careful using
sudo and only use it when absolutely required. Translated into English, it means 'Run this command but allow it to do anything it wants to my computer'. This is why you are prompted for your password.