Fish: Take care not to allow your fish to flop around and damage its scales and fins. Wrap the fish in a wet towel and seal the wrapped fish in a garbage bag. Remove as much air as possible from the bag. Place the wrapped and bagged fish in the freezer taking care to lay the fish out as straight as you can. when the wet towel freezes, it will protect the fish from damage and help to prevent freezer burn. Deliver to Taxidermist as soon as possible.
Birds: Avoid roughing up the feathers. Keep the bird as dry and clean as possible. If possible, gently tuck the head underneath a wing. Place the bird head end first inside a large zip lock bag, or garbage bag and remove as much air as possible prior to sealing. Freeze and deliver to Taxidermist as soon as possible.
Full Body Mammals: Perhaps the easiest of all in terms of handling in the field. Simply keep your animal as clean, dry and cool as possible. Place in a thick garbage bag. Remove as much air as possible prior to sealing the bag. Freeze and deliver to Taxidermist as soon as possible.
Reptiles: Same as Full Body Mammals. If the reptile happens to be venomous, tape the bag up and clearly label it as "VENOMOUS" It would also be very thoughtful of you to indicate which end of the bag the head is on:)
Insects /Crabs / Lobster: The larger varieties of insect such as Tarantula and some Scorpions can make attractive and unusual mounts. Crab and Lobster as well. Just Zip lock them with as little air as possible. Seal the zip locked bag in a protective container such as Tuper ware, or card board box that is strong enough to protect the delicate legs, claws, or tails from breakage while in the freezer, or in transit.
Game head mounts: First off, avoid dragging the animal if possible. Have you ever seen a deer head mount with a bald, or thin spot on the shoulder area? This was caused by carelessness while dragging the animal. After you have caped (Skinned) your animal, it needs to be kept as cool and dry as possible. Ideally, you need to get your skinning done, bag the cape, seal the bag, put it on ice and get it to the Taxidermist, or at least frozen A.S.A.P.