Natural light
I have a preference for using natural light as, over the years, I have found this gives me the best results and shows fungi as you would see them in their natural surroundings. Unfortunately, there is never enough light!
Finding the light
I look for a bush that has an open canopy that lets plenty of light down onto the forest floor. This has the advantage that lots of mosses tend to grow in this sort of habitat, which makes better and more colourful backgrounds for photos. Open forests are also easier to penetrate and allow you to go off the tracks to explore better. Be careful not to get lost!
Colour of light
I find it best to be out during midday when the sun is at its highest point and can penetrate the forest canopy. As the colour of the sun light also changes through the day, I avoid being out too early in the morning or late in the afternoon as this is when the sun is very yellow. There is also the problem of the tree leaves filtering out the green, giving your images an unnatural red cast. If your camera has a custom white balance setting, then it may be possible to compensate for this. Other wise, you may need to tweak the image at home in a graphics editor.
Try to get the available light coming from the front or off to the side of the fungi. Use a reflector to bounce light into shadow areas (opposite side or under the cap). Avoid very dark locations. The results are never very good. Even using a reflector does not help if there is no light.
From behind
If available light is coming from behind the fungi, you end up with the top of the fungi burnt out and the remainder in shadow. Even a reflector will not help to stop this. On the other hand, if the fungus is transparent, then this can be used to your advantage and be used to give the fungus a nice glow.
The disadvantage of using available light is the long exposure times that can cause reciprocity failure of the film or noise if using a digital camera. Noise refers to random pixels turning on or off during the exposure, giving a spectacled effect, particularly in the shadow areas. The higher the ISO, the more pronounced this is.
Using flash
I have a cannon MT-24EX flash unit for my camera that I have used from time to time but find the results are not always that good. Yet on the odd occasions when flash does work with good results, this only happens in dry conditions.
The advantage of using flash as the main lighting source rather than as a fill flash is that you are no longer burdened with carrying a heavy tripod or the time it takes to set up. Thus, it is an advantage when you are out with others who don't like to stop, like trampers and biologists.
There are a number of disadvantages to using flash, particularly in our wet and damp forest. Some of these are:

1: Light reflecting off glutinous caps and stalks.

2: Colours were brighter, washed out or with a distinct colour shift, possibly due to the transparent nature of fungi.

3: Burnt out highlights.

4: Light reflects off the wet moss in the foreground and background.
Colour change
Possum in the head lights effect.
Light reflecting of water droplets