Buy an external hard drive – USB is cheapest and, even though slower than FireWire or Thunderbolt – lightning fast is not essential for backups. I suggest you buy a disk at least double the size of the data on your HD.
Plug in the hard drive to your Apple Mac laptop or desktop and cancel any message to use this disk with Time Machine. Its not ideal running a PC formatted disk for Time Machine to backup a Mac and it could lead to problems in the future. If you get error message needs initialising ignore.
On your Mac go applications, utilities, & open disk utility.
There will be 1 icon in the LH column for your hard disk which will change to 2 icons once its initialised. Select top icon for this external disk.Once highlighted you will see some new headers on the RHS of this window.
Under volume scheme click current and select 1 Partition.
At the bottom of this column select options and click radio button for GUID Partition Table. Click OK.
On RHS under Volume Information name the disk something suitable e.g. TM backup.
Immediately below in Format select Mac OS Extended (Journaled).
Bottom right of this window click Apply and that’s your new hard disk ready to use on any Mac with an Intel processor.
Now open Time Machine from the icon top right of screen or from applications.
Under Options make sure the backup drive is in the excluded list and add any other drives you do not want to backup.
Select Disk button & select the new backup drive you have just formatted..
On screen you will see Next backup changes to 120 seconds and your Mac will start to backup then.
The first backup will take a long time. Depending on the size of the data you are backing up suggest for any first backup to set up & leave running overnight. After this first backup Time Machine will only take seconds in background to backup changes every hour.
If you need any help or further advice please contact me.
Or you could watch the screen movie below