So I created my own modified version of a program with the GPLv3, and it's open source and everything.  
My question is how am I supposed to state that I modified it?
Do I just put in a comment saying # Modified by yentup ?  
I've tried researching about this topic but I haven't found any directions on how to do so.
You have no requirement to say that you modified it at all - your only obligation is to offer the source code to anyone who uses your version.
However the best solution for you, the original authors and future users is probably to have your changes put back into the main source tree, assuming that they would be useful to other users! At which point you the version history would mark your changes, you could also add your name in a comment if you wished.
Is there a formal way to state modifications of a program covered with GPL?