I purchased a Macbook Pro (my first Mac) about a year ago, and I let a friend talk me into partitioning the hard drive as part of Apple's 'Time Machine' data backups. I think I'd rather store backups on an external drive - is there a simple way to undo or remove partitions or do I have to reformat my hard drive? If so, what's the best way to do that on a Mac?

Backup the data then you can use Disk utility to remove the partition by clicking on the drive (partitions will be listed below and going to the partition tab.
Backing up all data is a good idea when editing partitions.