EDITED to match edited requirements.
You can achieve exactly what you want by creating a Shared folder. To do so go to System Preferences > Sharing > File Sharing and Add all the folders you want to share.
You can do this, too, by directly selecting a folder in the Finder,, choosing Get Info from the File menu, and enable Shared Folder to share it (or deselect "Shared Folder" to stop sharing the folder).
Extracted from Apple's 101: File Sharing.
You can achieve this in a couple of ways.
Logging as root will grant you read and write privileges to all areas of the file system. You'll need to have the root user enabled. To do so, assuming you're using Lion:
- Go to System Prefereces > Accounts.
- Click the lock and authenticate with an administrator account.
- Click Login Options.
- Click the Edit or Join button at the bottom right.
- Open Directory Utility.
- Authenticate with an administration account.
- Choose Enable Root User from the Edit menu.
- Enter the root password.
Here is described for earlier OS.
Placing the file under the Shared Folder (/Users/Shared), or Sharing the folder, the one where the file you want to edit is, will grant other users access to that file. More about it, and how to Share other folders here.