Anyone recommend how a person could get started with autotools in building a C project?
Follow the autotools tutorial.
You can also get the autobook. Chapter 4 covers a minimal GNU autotools project.
I would recommend this tutorial and get the book when it's released. The tutorial really helped me a lot, it even contains a step by step conversion of an existing (non trivial) project to autotools.
Alexandre Duret-Lutz's tutorial is my resource of choice.
There are also:
To me, the autobook is not up to date anymore and more difficult to read. However it still contains interesting chapters like Writing Portable Bourne Shell.
Also, consider learning about non-recursive automake which addresses the concerns raised by Peter Miller in his Recursive Make Considered Harmful article.
EDIT: for reference, there is also Autotools Tutorial for Beginners.