What body parts are you looking to retrieve from the animal?
You need to ask yourself this question before you collect it. No good scraping up anything flat, it will be of no use to you. Skull shattered? did you want the skull? If not, what else can you collect from the animal?
How long do you estimate it to have been there?
If you only want bones, this doesn't really matter. But if you want skin/fur/paws/tails/wings/feet/whole heads , then you must not try to preserve anything over a day dead. It will have begun to decay and the smell will linger even after drying. The fresher the better
2 - Scrape it up.
For those of you who are able to drive, I would reccomend that you keep plastic sheeting in your car.
For those like myself, who are not able to drive, I personally always keep a few plastic grocery bags in every handbag I use on a regular basis , and also my workbag. You simply never know when you'll find something dead, and thus you will always have a bag or two handy.
Disposable gloves may be needed in the case of larger animals.
To pick up a small-ish body - It's exactly like scooping a dogshit. Put your hand in the grocery bag ( turn the bag inside out and make sure it has no holes or rips ) , pick up the body, and turn the bag the right way. This way you can retrieve the body quickly and cleanly, without touching it barehanded.
For larger animals - This will require the plastic sheeting and gloves . The best way would be to roll the animal onto the first third of the sheet, and then roll it up in the plastic before hoisting it into your car.
Things to watch out for
Bodily fluids and excreta - Blood, guts and shit basically. Make sure your plastic bag or sheet has no holes or rips !!! The body may be gassy or bloated depending on how decayed it is. Bloated bodies have been known to explode when moved, you are forewarned !
Smells - This will depend on how long the body has been there, and the level of stench in older bodies will be affected by heat and cold. The hotter it is, the smellier it will be.
Traffic - If the thing is in the middle of a busy road, LEAVE IT THERE. No matter how desirable it may be, no dead animal is worth getting mowed down for, and you may be arrested for obstructing traffic and distracting drivers. If you really must have the thing, return in the small hours of the night, when roads are quieter and usually safer, and retrieve the body as quickly and safely as you are able. Be aware that it's condition may be worse than when you first saw it, as people may have driven over it even more during the elapsed time.
Police officers - To my knowledge it's not illegal to pick up roadkill. It saves the local road cleaners a job if nothing else. But if you are unsure, check with your local authorities beforehand. They will probably think you are insane.
Burial - I have an area of my garden where I bury my bodies, those with limited or no garden space should find buckets or large plastic storage tubs ( the deep lidded sort you put old crap in and stick in the attic ) to be a cheap and easy option. I dig a hole about 8-10 inches deep. For a bucket, put it close to the bottom about 1/3 of the way from the base.
Soil . The type of soil you have may affect the speed of decay. Very sandy/salty coastal soil or boggy peat rich soil, may slow down the decay of the body. Human bodies have been found on/near beaches and peat bogs, effectively preserved by the type of earth they are buried in ( some are over 2000 years old, such as the Lindow bodies ) If you have such an unsuitable soil, then buy yourself a cheap bag of potting soil or compost to put in your buckets.
Additions and helpers - Got ants nests? Use them ! Bury your body close to the nest, the ants should help with stripping the flesh away. You could also try purchasing some fishing maggots, chuck them onto your body, and cover with a few inches…