How to do time machine back up?

You should get a prompt asking if you want to inherit an existing backup, or start a new one. But I have seen reports of people saying they never saw that prompt and the drive got wiped.

Here is what I would do, just to be safe.

Make sure TM is turned off, then attach your drive. Open Disk Util and look at how much space is currently being used on the drive by the backup. Let's just say it is 320GB for example.

Now use Disk Util to shrink down that single partition to a little over 320... say make it 350GB. Just follow this guide to resize the partition. This will not erase your data.

Now click the + at the bottom to add a second partition of whatever size you want. You can add one of 650GB (using my example) if you like to use up the rest of the drive. Just name it whatever you want as long as it is different than the first partition, then click apply.

Now go back to TM click the select disk button then select your new partition, then turn on TM. This will ensure the new TM backup is o the second partition and your old backup is untouched on the first partition.