Do you have a specific debugger in mind, or are you just looking for a general introduction to debuggers?
You'll almost certainly be right to debug Linux Checkers, you'll use GDB, and this is a good tutorial (but don't let it stop you from googling ;-) http://www.google.com.sg/search?hl=en&source=hp&q=gdb + tutorial
I don’t know how you develop your code, but I highly recommend using the Eclipse IDE * to use the CDT plugin since you are developing C) - http://www.eclipse.org/cdt/
Eclipse is a great free IDE and is almost a de facto standard among professionals. You can edit your code and also go through it in the Eclipse debugger, but Eclipse also supports many, many other plugins that will be very useful to you:
DoxyGen for documenting your code, Splint for analyzing static code, problems with traps that are not a compiler, CppUnit for automatic testing, BugZilla (etc.) for reporting problems, CVS, Subversion, etc. for version control ... you get an image.
, , Eclipse DDD, , DDD, .. http://www.gnu.org/software/ddd/all.png
? , DDD , IMO.
, , , (http://www.splint.org/ http://sourceforge.net/apps/mediawiki/cppcheck/index.php?title=Main_Page) ..