Time Machine doesn't work with an iPod Touch which is where you've posted this question.
Time Machine works with your computer to backup your hard drive to another hard drive. It is just a backup utility like many others.
For some people Time Machine will be more than adequate. Time Machine is part of OS X. There are two components: 1. A Time Machine preferences panel as part of System Preferences; and, 2. A Time Machine application located in the Applications folder. It is used to manage backups and to restore backups. Time Machine requires a backup drive that is at least twice the capacity of the drive being backed up.
Alternatively, get an external drive at least equal in size to the internal hard drive and make (and maintain) a bootable clone/backup. You can make a bootable clone using the Restore option of Disk Utility. You can also make and maintain clones with good backup software. My personal recommendations are (order is not significant):
Although you can buy a complete external drive system, you can also put one together if you are so inclined. It's relatively easy and only requires a Phillips head screwdriver (typically.) You can purchase hard drives separately. This gives you an opportunity to shop for the best prices on a hard drive of your choice. Reliable brands include Seagate, Hitachi, Western Digital, Toshiba, and Fujitsu. You can find reviews and benchmarks on many drives at Storage Review.
Enclosures for FireWire and USB are readily available. You can find only FireWire enclosures, only USB enclosures, and enclosures that feature multiple ports. I would stress getting enclosures that use the Oxford chipsets especially for Firewire drives (911, 921, 922, for example.) You can find enclosures at places such as;
All you need do is remove a case cover, mount the hard drive in the enclosure and connect the cables, then re-attach the case cover. Usually the only tool required is a small or medium Phillips screwdriver.