You have to have a hard drive to use for the backup. A Time Capsule is a network storage drive that also acts as a network router. If you already have a router, then you don't need a Time Capsule just for backup.
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;
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):
2. Data Backup
3. Deja Vu
5. Synk Pro
Visit The XLab FAQs and read the FAQ on backup and restore. Also read How to Back Up and Restore Your Files. For help with using Time Machine visit Pondini's Time Machine FAQ for help with all things Time Machine.
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;
1. Cool Drives
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.
If you have a regular router (not a Time Capsule) then you can't use it for backup. The Time Capsule is a specialized device that combines the functions of the Airport Extreme Base Station router with a hard drive that connects to your network so you can backup a computer wirelessly to the hard drive. Unlike a standalone backup drive, a network drive can be accessed by multiple users through the local network. However, because network backup is usually done wirelessly it is very slow compared to a standalone hard drive connected directly to your computer.
If you only have one computer to backup, then it's just as easy and less expensive to buy a separate hard drive. Also, a light weight separate drive is easy to carry around if you need to. Not so of a Time Capsule.