1. Use a tripod
Because light levels drop quickly when you're going deeper into the forest, shutter speeds will rise fastly. Use a tripod for pin sharp results.2. Bring your cirulair polarizer
With a lots of greens and in during autumn reds and yellow, you can saturate them more by using a circulair polarizer. Don't forget to reposition the polarizer each time. Be aware light levels will drop even more with the use of the polarizer and it can add up to 2 stops of shutter speed (=it makes your shutter speed 4x slower).
3. Explore vertical compositions
Make use of vertical compositions as well. It creates a sense of depth and it can make look trees taller and more dramatic. Try to reframe each horizontal landscape shot with a vertical portrait composition to explore the possibilities.
4. Embrace overcast days
Especially on bright overcast days, you can get great forest shots. Due to the lack of direct sunlight, you don't get harsh shadows and burned out highlights. The clouds are working like a huge softbox to diffuse the light.
5. Enjoy some rain
Even with some slight rain, you can get great vibrant forest photos. The rain will saturate the colors naturally. If you're lucky and you'll stay dry under the trees.
6. Find natural lines
Forests can be very chaotic, so find natural lins or ordering to get a clear composition. E.g. use a dirt road or a creek as a lead in line. Move around carefully to order trees up into a row, etc. One small step can make a big difference.
7. Change perspective
Use a long lens to tighten trees together. I will look like the trees are more together and this creates a sense of depth. With a wide angle lens, get down to the ground to emphasize the the foreground.8. Get the most out of sunrise and sunset
During sunrise or sunset, stay close to the edge of the forest to get the most out of the beautiful light at this time of the day. Deeper into the forest, there's less sunlight and it's harder to find places where you get the right light.
9. Use side lighting
When using side lighting, trees getting a nice 3D look and look round in the end result. With front lighting the trunk will be evenly lit and look flat. With side light the trunk goes from light to dark and will look round. On an overcast day use a compass to determine where the light is coming from.
10. Bring in a human element
A person in the frame, even very small, can create a focal point. You can also use a self timer and position yourself into the frame to emphasize the size of trees or wideness of an area.
Bonus Tip
And last but not least: leave enough bread crumbs behind to find your way back ;-)