Q: Use Time Machine without Internet?

Yes. But your backup drive must be connected to the computer. You can use USB, Firewire, or Thunderbolt depending upon what is available on the computer.

The "Book" on Time Machine (Mountain Lion)

OS X Mountain Lion: Time Machine overview

Mac Basics: Time Machine

iTunes 11 for Mac: Time Machine

Mac OS X: Time Machine Basics

OS X Mountain Lion: Time Machine preferences

OS X Mountain Lion: Time Machine problems

OS X Mountain Lion: Time Machine configuration preferences

OS X Mountain Lion: Time Machine options preferences

OS X Mountain Lion: If Time Machine is slow

OS X Mountain Lion: About the Time Machine backup password

OS X Mountain Lion: Back up files with Time Machine

OS X Mountain Lion: Exclude items from a Time Machine backup

OS X Mountain Lion: If a Time Machine backup is interrupted

OS X Mountain Lion: Disks you can use with Time Machine

OS X Mountain Lion: Restore items backed up with Time Machine

OS X Mountain Lion: Pause and resume a Time Machine backup

OS X Mountain Lion: Recover items using Time Machine and Spotlight

OS X Mountain Lion: If Time Machine doesn’t back up certain files

OS X Mountain Lion: If Time Machine can’t find your backup disk

OS X: Cannot install on a volume used by Time Machine for backups

OS X Mountain Lion: If Time Machine remains in the “preparing” stage

OS X Mountain Lion: If your Time Machine backup disk runs out of space

Time Machine: How to transfer Time Machine backups from one Time Capsule to a different one

Time Machine: How to transfer backups from the current backup drive to a new backup drive

Mac OS X v10.6: Issues after restoring a Mac from a Time Machine backup made with a different Mac ("Restore System From Backup…")

The Second Book of Time Machine is: Pondini's Time Machine FAQ for help with all things Time Machine.

Mac Basics- Time Machine

Time Machine - 101 Tutorial

Any directions on how to use Time Machine to back up my desktop would be much appreciated.

 

Do you mean a time capsule.. ie the hard ware device.. Time Machine is software that does the backup on the computer.

You can use a TC only as network device. .but it is possible to do it and still get internet at the same time via wireless.

See the instructions in this thread.

https://discussions.apple.com/thread/4817218?tstart=30

I can help if there is something you don't follow but I gave a goodly lot of screenshots there so I hope it makes sense..

Nonetheless, it is much better to use a FW800 or USB drive on the desktop Mac.. faster, more reliable and far cheaper.. just ebay the TC if it is no good to you. That will cover the cost of the USB external drive or whatever you choose.