My process changes from year to year and game to game. It depends on the game and what the focus is. For Blackwell, the focus was always the character and the dialog, so I always wrote that first. For Unavowed, I really want to focus on the exploration and interactive elements before the dialog, so I make sure to get that solid before homing in on the dialog stuff.
For example, I usually start by sketching out ideas in my notebook. Most everything I cross out, but eventually something coalesces into something I think is good. Like this fight with a sea monster:

Then I open up MS Paint and start making placeholder graphics and implementing puzzles and designs.

I figure if I can make a scene with my crappy line drawings and STILL make it fun and interesting, then I'm confident enough to move on to final art:

(ended up putting the monster to the BACK of the boat so we could have a chase scene instead)
Then I start writing all the dialog and flavor text to support it.
And then for the next game I will do it all differently!
For example, I usually start by sketching out ideas in my notebook. Most everything I cross out, but eventually something coalesces into something I think is good. Like this fight with a sea monster:

Then I open up MS Paint and start making placeholder graphics and implementing puzzles and designs.

I figure if I can make a scene with my crappy line drawings and STILL make it fun and interesting, then I'm confident enough to move on to final art:

(ended up putting the monster to the BACK of the boat so we could have a chase scene instead)
Then I start writing all the dialog and flavor text to support it.
And then for the next game I will do it all differently!