A Lightning rod is fixed to the building and it is not given earthing then what happens? How does the lightning reach the ground through the building?
A Lightning rod without earthing is as good as any other conductor laying stray in open. If its not earthed then it wont work at all. There is nothing very fancy about the whole process. You need to connect both ends of a circuit to make current flow. An improper grounding connection can cause disaster sometimes as the lightening may find another route like plumbing to reach to the ground, which will produce the same effect as that of a lightning striking any building and can result in fire. Even simple grounding is not advisable for such a system. The area at the place of grounding is treated with saline water to increase conductivity.
Many times improper grounding renders the whole system inappropriate. Even sharp curves are avoided in the conductor connecting to the ground to reduce inductance. If ever curves are made then the radius is kept large to decrease inductance.
Any lightning protection system which includes a lightning rod will have the lightning rod galvanically connected to ground. Usually this is done with very heavy gauge copper or aluminum wire which goes directly to a buried metal rod (typically copper). But some designs use the steel in steel-girder construction buildings as the path to ground. Some U.S. government/military buildings have many grounding points (reference MIL-HDBK-419, Volumes I and II).
A lightning rod, whether grounded or ungrounded, which is higher than the rest of the building, will attract more lightning to that building. A lightning rod which is otherwise correctly installed, but which is ungrounded, serves the purpose of attracting more lightning to an unprotected building. The lightning ~WILL~ find a path from the rod to ground. And, since a proper path has not been provided, the path found will almost certainly be through places in the building which you don't want it to go.
You ask how lightning passes through the building to ground. That is a huge questions with many answers. You might have better asked how it crosses the vast expanse of sky to get to the rod in the first place. That, believe it or not, is the easier question to answer. The practical answer to your question is that lighning does a lot of very wierd stuff. It does NOT necessarily follow the path of least resistance. I'd be guessing, but I'd like to say it follows the path of least impedance. In any case, if you do not give it a low impedance path to ground, it will find the next lowest... even if the next lowest is not low at all. That's where you find stories of lightning passing through doors, windows, bathtubs, plumbing, people, pets, mattresses, wooden studs, concrete, and the like.