Inability to partition an external hard disk

I've just attached an external hard disk to my iMac and have been struggling in vain to partition it. The drill, I understand is to go into the Disk Utility, select the disk you want to partition then click "partition" on the right hand side of the screen, but despite several attempts I've never been able to find "partition" on the screen. I guess I must have done something wrong somewhere, but how can I fix this problem?

Connect the Drive> Open Disk Utility> Click the connected drive> Format it to Mac OS Extended> Then partition it?

As above - if the external drive is formatted to NTFS you will be unable to do anything with it except to read from it. It has to be formatted to the Mac OS Extended Journaled file format or FAT-32 first. Then you can do the partitioning.