I recently found this relationship chart which I love because it allows me to quickly determine that if a match is a 3rd. cousin we share 2nd great-grandparents. If the match is a 4th cousin we share 3rd great-grandparents. It's not that complicated and I wish I could remember that the common ancestor is one number less than the cousinship... but my brain won't retain that.
On the chart I'm using, you simply look for the projected relationship, so let's say your DNA match was 5th cousin - look on the chart for 5th cousin (it is row 7, column 7). Now look UP to the top row, which in this case says "4th great-grandson or daughter". Okay that means you and your match share 4th great-grandparents. See how easy it is?
There are other charts online for understanding the term "cousin removed" and for figuring out the relationship of a person if you know their ancestry and how it connects into your family.