Mummification is the act of preserving a deceased human's (or animal's) corpse by means of drying it and denaturing it. The organs in the body were preserved in varying ways as the mummification process evolved. When the person died, and how rich they were decided the quality with which they would be mummified.
Perhaps the most well known method was the use of Canopic Jars. These were used to hold the lungs, liver, stomach and intestines of the deceased seperately. Initially these jars usually had lids which were either representations of the deceased, or of the Four sons of Horus. The lids were miniature busts of the four sons, and some were extremely detailed.
In certain burials, such as those of the Pharaohs, the provision for the protection of the internal organs was often more sophisticated. This Canopic Coffin is one of a set found in the tomb of Tutankhamun. The embalmed organs were placed inside the coffins which were then put into an alabaster canopic chest with the four stoppers carved with the Pharaohs likeness.
In an alternative method the internal organs were placed in a solution of Natron salt and interred in a special Canopic Chest, or returned to the body cavity. Natron salt dries out the body by removing water from the each of the cells, so that when the body is removed from the solution bath it will quickly loose any remaining moisture. In these cases, dummy canopic jars may have also been included in the tomb.
In later periods the processes used seem to have decreased in complexity. In the later dynasties a liquid similar to Turpentine was injected up the rectum of the deceased. This liquid dissolved the soft internal organs and was then drained, organs and all. This did not leave enough of the organ left to put in jars, and so it was not very popular with the extremely rich.
In cases where the internal organs were not left in place, or returned after treatment, the body cavity was packed with a filler. They used anything that would harden into a semi-sturdy packing: mud, resin-soaked linen, clay, even a crude cement of pebbles and clay.
Another process was to remove the internal organs, mummify them individually, then return them to the body cavity. In many cases figures of the Sons of Horus were included with the packages. These figures are clearly visible on some mummy X-Rays.
After the body was dried out the fingers and toes were individually wrapped, then each limb was wrapped on top.
During the drying process, when the body was desiccated in Natron, it was noted by the embalmers that the finger and toe nails could fall off. It later became common practice towards the end of the Middle Kingdom to tie the nails on with string or a waxy ribbon.
A recent study as part of the NMS Mummy Project in Edinburgh involved detailed examination of a mummy which had been previously unwrapped. The body was found to be so well preserved that fingerprints were still visible. Another common practice in richer burials was to cover the fingers and toes in metal caps to preserve their look. Pharaoh Tutankhamun had a full set of gold covers of this type which were discovered when the mummy was unwrapped by Howard Carter.
In some cases the removed and individually embalmed internal organs were packaged and placed between the mummies knees, secured by more layers of wrapping.
The wrappings themselves consisted of fine linen coated in resin, although the mummies of poorer individuals were wrapped in a variety of materials; mostly whatever the family could find around that would do the job. One set of bandages removed when a mummy was unwrapped were reconstructed into a complete square rigged sail.
When a body was mummified the internal organs were usually preserved in some way. This was not true of the brain which was often just discarded. This was usually done by inserting a hook up the nose and using it to slice up and remove the brain tissue, with the cavity then being washed out. The reason for this treatment of the brain was that the Ancient Egyptians believed that it was the heart which was where the 'soul' lived.
Many of the mummies which have been examined show damage to the skull in the region of the nose proving that this was the method used. The mummy of Rameses II had peppercorns inserted into the nasal cavity in an attempt to retain his distinctive hooked nose.
This was not always the case. Full mummification would have been quite an expensive process, out of the reach of many of the ordinary people. In certain cases the brain was left inside the skull, where it then dried and shrunk. This could produce a rather novel rattle.
It was important that when the spirit, or "Ba" of the dead person returned, the body could be recognised. This was the reason for the elaborate masks placed over the head of the mummy.
It was also believed that if the body was destroyed the spirit could not live on, and for this reason burials often included a reserve head or a statue that the spirit could inhabit should the anything happen to the mummy. It is possible that many of the mummys presently 'missing' could have been destroyed in antiquity deny their spirits this eternal life.
As rk2001 said, a complete mummification took about 70 days to do. However, that is only a purely actional mummification, the way a scientist would do it. The Egyptians saw mummification as a ceremony, and therefore it was broken up between each step by one or two day prayers, and so a traditional ceremonial mummification took around 130-150 days.
Class notes from an egyptology class I took at my local library. Also some paraphrasing from "http://www.akhet.co.uk/clikmumm.htm" Bugs go to Jaybonci