If you plug an external hard disk into your mac via USB or Firewire, then you should see it show up in Disk Utility - period. If it does not show up in disk utility then there is likely a problem of concern with either the Mac, the external drive, or the cable you're using to connect them. If you can see the disk in Disk Utility when you connect it to another Mac, then the problem may be with your Mac. If you can see some other external disk in Disc Utility when you connected it to your mac (or to another mac) then the problem may well be with the drive you are trying to use. If you can't get either of those to work, try using a different cable.
Once you can see the drive in Disk Utility, then you can format using the "erase" option for use by Time Machine . You should create a MacOS HFS+ Journaled partition (or just format the entire drive that way) if you intend to use it for Time Machine. I do NOT recommend you plan to use TimeMachine for remote backup over a wireless connection unless you plan to do so using Apple's Time Capsule device, rather than just some random hard drive. Last I read, Apple didn't recommend it either and would not support it; though that may have since changed.
In general, I also do NOT recommend relying on Time Machine as your sole option for backup. Time Machine is a best-in-class solution on the Mac for retrieving an older version of a file that you have since changed or deleted. It is not a great solution in my opinion for making a comprehensive backup in case of drive failure... And all hard drives will eventually fail; it's a matter of "when" not "if". For that unfortunate scenario I recommend you make periodic clone backups with a program such as SuperDuper! or Carbon Copy Cloner. Another alternative if you'd like a continuous backup solution that offers similar convenience and functionality of Time Machine is to use CrashPlan from CrashPlan.com -- the software for all of these is options is free. In the case of CrashPlan you need not, and they even recommend that you are better off not to, rely on their remote backup servers for storage. Find yourself a backup buddy, or another Mac, PC, or Unix computer at work or home and incrementally backup to your external hard drive after connecting it to that machine ... either over the internet, or any wired or wireless connection using CrashPlan. CrashPlan will allow you to make your initial Backup direct to your drive on your local machine via a USB or Firewire connection, and then keep it up to date remotely after you relocate it. If you need to recover someday, you can bring back the drive and do a fast, immediate restore. If you just need a couple files you can grab them remotely over the net just as you would with Time Machine.
If you'd like an opinion from a more authoritative source then I recommend you read comments from Adam Engst and Joe Kissel who published in Tidbits how CrashPlan allowed them to recover all their data when Time Machine failed to do so. Luckily they were using both. The net is littered with disaster stories where Time Machine has failed.
In summary, if you want comprehensive backup, I recommend:
* Periodic clone backups for instant-up restore in case of disaster.
* Time Machine for convenient recovery of few changed or deleted files.
* CrashPlan as a painless set-and-forget means for free off-site storage.
If you want a less comprehensive solution, you can choose not to implement all three.
Hope this helps; happy to answer any more questions about backup.
Once you can see the drive in Disk Utility, then you can format using the "erase" option for use by Time Machine . You should create a MacOS HFS+ Journaled partition (or just format the entire drive that way) if you intend to use it for Time Machine. I do NOT recommend you plan to use TimeMachine for remote backup over a wireless connection unless you plan to do so using Apple's Time Capsule device, rather than just some random hard drive. Last I read, Apple didn't recommend it either and would not support it; though that may have since changed.
In general, I also do NOT recommend relying on Time Machine as your sole option for backup. Time Machine is a best-in-class solution on the Mac for retrieving an older version of a file that you have since changed or deleted. It is not a great solution in my opinion for making a comprehensive backup in case of drive failure... And all hard drives will eventually fail; it's a matter of "when" not "if". For that unfortunate scenario I recommend you make periodic clone backups with a program such as SuperDuper! or Carbon Copy Cloner. Another alternative if you'd like a continuous backup solution that offers similar convenience and functionality of Time Machine is to use CrashPlan from CrashPlan.com -- the software for all of these is options is free. In the case of CrashPlan you need not, and they even recommend that you are better off not to, rely on their remote backup servers for storage. Find yourself a backup buddy, or another Mac, PC, or Unix computer at work or home and incrementally backup to your external hard drive after connecting it to that machine ... either over the internet, or any wired or wireless connection using CrashPlan. CrashPlan will allow you to make your initial Backup direct to your drive on your local machine via a USB or Firewire connection, and then keep it up to date remotely after you relocate it. If you need to recover someday, you can bring back the drive and do a fast, immediate restore. If you just need a couple files you can grab them remotely over the net just as you would with Time Machine.
If you'd like an opinion from a more authoritative source then I recommend you read comments from Adam Engst and Joe Kissel who published in Tidbits how CrashPlan allowed them to recover all their data when Time Machine failed to do so. Luckily they were using both. The net is littered with disaster stories where Time Machine has failed.
In summary, if you want comprehensive backup, I recommend:
* Periodic clone backups for instant-up restore in case of disaster.
* Time Machine for convenient recovery of few changed or deleted files.
* CrashPlan as a painless set-and-forget means for free off-site storage.
If you want a less comprehensive solution, you can choose not to implement all three.
Hope this helps; happy to answer any more questions about backup.