I have done just finished drying four rabbit skins. I got them home on a sunday evening so couldn't use a chemical method as I couldn't purchase them time, so i laid them out flat and salted them. The next day I removed that layer of salt and gently removed what ever soft fat I could find. I then re-salted. The next day I scraped off the salt gently and then re-salted. I did this for the next two days (so 4 days of salting and resalting).
When the skins were completely dry I scraped of the papery inner very gently with mussel shells. I put holes in youngest looking bunny skin. The fattiest skin still had a slight aroma after a week so I completely dried using a mugwort smoke fire. I found if i kept sniffing the hides I could detect if they weren't dry properly in places and pay extra attention to those areas.
It is first time i have ever done skins but they are holding their hair, and don't smell in anyway. I got this method off an old post by paganwolf:notworthy , and i am really glad of it as there are many methods and it can be confusing. This one won out as it is based on what I had in my cupboard at the time. It is simple and it worked, I don't know if it would work with a thicker animal, but i am no expert. But there are alot of differant methods and some things can only be learned by experience.
My next step is tanning the hide with stewed oak.
This website has a mass a information on natural methods, and really good tips like use hairdryer when the wife is not in the house.
http://www.braintan.com/articles/index.htm