The Blue Forest is an area in the Eden Valley region of Wyoming where spectacularly preserved petrified wood can be found. The directions to get there are a bit winding and once you get there you may be a little confused by the relatively flat terrain.
View of the area
It's called the Blue Forest because the fossils are often preserved with a ring of blue chalcedony around a gray/black opal replaced fossil wood. You can see piles of dirt and the holes the came from all over the nearby area. You can search the surface and dirt/rock piles for shards of discarded fossil wood/agate but to find whole branches or trunks of wood you have to dig into the rock layers beneath your feet.
A typical trench/hole:
Millions of years ago this area was a seasonal swamp that was part of the ancient Lake Gosiute. Logs and branches would fall into the water and sink to the bottom but were not always quickly buried. The wood became waterlogged and algae would grow on the surface forming Stromatolite like coatings. Eventually both the algae and wood were buried and became replaced with Silica percolating through the ground water. When you are digging you'll find the Stromatolite layers first but you don't know how big a piece of wood you've found yet because the layers thickness can vary.
Here you can see thick layers of Stromatolite that built up on a thin branch.
Experience will help you determine how best to dig out the fossils and how thick a piece of wood you have under all the layers of Stromatolite. Once you get the fossils out of the ground they will cut and polish very nicely since it's agate.
I've not stayed at the site of the Blue Forest long enough to try my had at extensive digging but here is a picture of some pieces of wood I found on the surface.