Taking ownership of files in Windows is necessary to edit or delete system or program files that you have no access to by default. There are multiple ways to achieve that goal, like doing everything manually through the Properties menu, applying a registry tweak or, as described here, executing a command in the Command Prompt. Note that taking ownership will not let you edit every system file. Windows has set precautions so that you don't edit any of the most important files which may be helpful in some cases but can be really, really annoying in other.
To start off, you need an elevated command prompt which is simply a command prompt opened as administrator. In Windows 8 you can open that by right-clicking the bottom left corner of the screen and selecting Command Prompt (Admin). In Windows 7 and previous, search the main menu for cmd, right-click it and select Open as administrator.
You need two commands now: one to actually take ownership of the file or folder and one to grant yourself access rights. These are the two commands you will want to use:
For folders, use:
takeown /f folder_name /r /d y
icacls folder_name /grant username_or_usergroup:F /t /q
For files, use:
takeown /f file_name /d y
icacls file_name /grant username_or_usergroup:F /q
The commands basically only differ in a few switches that make the folder procession run recursively. If you want to edit only one folder instead of the whole recursive lot, remove the /r and /t switches from the commands. For more info on the commands, simply enter takeown /? or icacls /? into the command prompt.
If I wanted to take control of my Program Files folder, I'd need to enter the following:
takeown /f "C:\Program Files" /r /d y
icacls "C:\Program Files" /grant christian:F /t /q