I know that the card parasite can potentially trash ice, but is there any other way? (I've just recently started playing)
I believe the only three current cards that can trash ICE after it's installed are:
In addition, there are other cards (e.g. Imp, Demolition Run) that can trash cards that cannot normally be trashed - such as ICE - from HQ or R&D, preventing them from being installed in the first place.