You're probably having trouble because you're trying to partition your startup drive, which you can't do--repartitioning with Disk Utility completely erases the drive you're partitioning, and that of course isn't an option if you're booted from the drive.
Assuming it's a second internal drive or an external, it's usually quite easy: Open Disk Utility, click on the drive's hardware name in the left pane (not the volume name, which is indented under the hardware, but whatever the top thing is--it'll usually give some model number). Then select the Partition tab to the right, select a partition scheme, and click the "Partition" button down in the lower righthand corner. You'll get a warning that you're about to completely wipe out all data on the drive, and if that's ok and you click "ok", then a minute later you should have your partitioned drive.
If you have an Intel Mac and are trying to partition your boot drive for BootCamp, then you need to use the BootCamp beta installer, not Disk Utility--it has a special tool that allows you to partition the startup disk without destroying the data on it.
