If I want to completely uninstall an application from the home screen or list of applications; how do I do it?
You can uninstall an application from the Market or from the Manage Applications settings screen.
From Manage Applications:
EDIT: I wanted to add a 3rd method that Rohan Singh had in his answer.
From your Home screen:
Go to settings->Applications->Manage applications
Select the application you want to remove.
Not all applications may be removed (some are locked down by your carrier / phone vendor).
A quick, easy way to uninstall an application is to hold down on its icon, and then drag it to the trash can at the bottom of the screen like you would if you were removing a shortcut from your home screen. However, hold the icon over the trash can for a few seconds until "Drop to uninstall" appears.
By using adb from command line:
adb uninstall <package name to uninstall>