Welcome to All Things Plants,
@attardam !
If you were seeing mushrooms and "fuzzy white stuff which looked like fine spider webs" (which I'm pretty sure was a type of mold, not moss), your terrarium was severely over-watered. Can you tell us a little bit more about your terrarium? Is it pretty much closed up, or is there a good-sized opening? (As Chillybean said, if you can try to re-post the pictures it would be helpful.) Another issue could be what type of plants are you trying to grow? Also, what sort of soil did you use? I've always used a layer of aquarium gravel, then a thin layer of activated charcoal, then a layer of potting soil for terrariums.
With the limited information that we have, my first thought is that your best course of action would be to completely start over (salvaging any plants that seem healthy), with new soil and a well-cleaned container. There are plenty of people on ATP with experience in planting terrariums, so I hope you will get lots of helpful answers here!
