Fresh and decayed corpses are those that still have flesh upon them. If their decay is advanced, or if you wish a skeletal servant instead, place the corpse along a coast or in a swamp or marsh. Animals are the Necromancer's greatest allies when it comes to stripping the flesh from a corpse. The ravenous mudcrabs of Morrowind can strip a corpse down to its bones in a matter of days. Lesser crabs in other provinces can do the same in a matter of weeks.
If you wish to create a zombie servant, one need only bring the corpse to a suitable site and enact the proper rituals. However, there are a few tips that a young Necromancer might want to know. For instance, a decayed servant may be raised many times, even if they have been dismembered by those who do not appreciate our Art. If one of your servants comes to an unfortunate end, you may raise the servant again by carefully gathering as many parts as you can find, binding the bones with leather straps, and sewing the flesh (if it not too decayed) with catgut. Your servant may be weaker each time this is done, but with care and maintenance, one may raise zombies dozens of times.
However, creating a mere zombie is a method best left to lazy or desperate practitioners. With only a bit more time and effort, one may create a far more useful mummified servant.
The first step to creating a mummified servant is to soak the decaying corpse in a bath of salt or natron for at least one month. This will halt the decay of the corpse, and if the corpse is fresh enough to have an unpleasant odor, the salts will remove that as well. In a moist climate, such as Argonian or Thras, you may have to apply more salts if they become saturated. Some Necromancers remove the vital organs before or after this process, but I have never found any practical reason for doing this.
The next step is to wrap the servant in cloth or linen. This will further preserve the body against decay and, if done properly, will offer some protection as well. Do not worry if the corpse seems too stiff or desiccated to be a useful servant, the proper rituals will imbue the mummified corpse with the strength to move itself. Most importantly, you will have a much stronger servant who will follow your commands with more independence and understanding.