The easiest way to go through it is to really just download an existing graphics set and use it as a base for creating your own. Play with it first, so you can get an idea of what tiles are used for what things.
For normal stuff, it's actually as easy as simply replacing pictures tile by tile with your own. No need to edit anything in the text. Use
this page in the Wiki as a reference for what gets used for what. Note however that some graphics set changes which tile gets used for what, so compare it first with the graphics set you're using as the base. I recommend you do this first until you start to see how your changes affect the game.
If you need to do advanced editing (like changing background and foreground colors in some tiles, or reassigning an object to a different tile number), the text files you will need to edit are in the
raw/graphics/ folder as well as
raw/objects/ folders.
But what text file to change varies by what tile you want to change. For example, for plants you edit the
plant_standard.txt while for creatures you do what sackhead posted above, etc. It's too complicated to explain I think. So it's best if you ask about them individually if you want to change anything (e.g. "I want to change the foreground color used for dead larch trees" or "I want to change the tile used for peasants", etc.). We should be able to answer those by then.
Also
my own thread last year asking the same questions might help you answer some of these questions.