The main NES homebrew forum is Membler's site  www.nesdev.com

Coding a homebrew is typically done in 6502 assembly language.   

A lot of people use nesasm as their assembler. 
I use CA65, which is more complicated to get working.
I believe there are some simple getting started tutorials which will help to get something visible on the screen.

So far, my attempts at homebrew have been relatively simple games or tech demos.

Al

To manipulate graphics, a lot of people use Tile Layer Pro
You can download it from a link on here:
http://www.zophar.net/utilities/graphutil.html

nesasm is the most commonly used assembler
Bunnyboy has made improvements to it and is available at his site:
http://www.nespowerpak.com/nesasm/NESASM3.zip

gbaguy had an old tutorial.  Most people suggest not using it since its old and some of the data has now been discovered to be wrong.

bunnyboy has a newer "nerdy nights" tutorial.
If you decide to try CA65, the nerdy nights stuff sample code was converted to CA65 by someone here
https://bitbucket.org/ddribin/nerdy-nights/overview

Al