I might be wrong on this, but it sounds to me like you have got mosquito larvae in your tank; if this is the case, they provide excellent food for any fish.
If they are mosquito larvae, they will rapidly swim down from the surface of the water if you disturb the water. They inhale air with a siphon placed next to their anus, so they are hanging head down from the surface.
If this is the wrong type, you have to give more details in your question for me to solve it.
You clean the tank as normal and vacuum the gravel and clean the pump and filter.
Cyclops are fishfood, so your fish will remove them, it will probably be a lot of living things in the gravel your fish will eat this too.
Parasites need fish and die without them, so this is normally not a problem when you restart your tank after it has been unused for some time.
Remember: before you add new fish to your tank you need to cycle it, this is to build a healthy bacterial flora to handle the waste from your fish and food.
You can read how this is done in this article; pet stores do often not inform you about this, but it is very important to know if you want to keep the fish alive.