For a comprehensive guide, see my Not A WalkthroughTM
list. It walks you through the entire game, including other story-related and collectible achievements.
Part 1: Blair Witch Not A Walkthrough - Part 1 - Beginning to Truck Fuse Puzzle
Part 2: Blair Witch Not A Walkthrough - Part 2 - Truck Fuse Puzzle to Rail Track
Part 3: Blair Witch Not A Walkthrough - Part 3 - Rail Track to Third Campsite
Part 4: Blair Witch Not A Walkthrough - Part 4 - Third Campsite to Finale
It's harder to be stealthy in the early game, but gets much easier after you get the new camcorder. Avoid every monster and don't shine a light on them. The best way to do this is to just never use your flashlight and rely on your camcorder's night vision the entire game.
You should only do this in a second playthrough since certain areas, particularly the Maintenance Shed and Camp B, can be difficult to find your way even when you have light. Using a flashlight in these areas will wake the monsters, and you won't be able to escape them without killing them (which you don't want to do).
Suggestions from the comments: crank up the brightness in the game, and don't use the rail car when you go to the Maintenance Shed and Camp B. In some sections, I did use my flashlight to get a feel for the area, let them kill me, then redo it.
Pay attention to Bullet, especially when he growls. He will point at monsters that you may not otherwise see. Don't worry if your screen starts flickering (you won't be able to avoid this), it's only when the screen turns red that you're being hunted. At that point, just let them kill you and restart your area.