How did the crust get on the earth?

I think your question is how did the crust originate. Scientists believe our planet originated about 4.5 billion years ago, and was extremely hot. The outer layer began to cool first, but extremely slowly. The outer layer, is called the crust, and ranges from 10 to 70 km thick. (see link) The crust is formed by the cooling of the earth, which is still going on.

You should think of the crust as the thin, outer layer, but its a bit more complicated. However, scientists in the last 50 years came to the conclusion that this outer layer was composed of large sections or plates and were capable of moving, albeit extremely slowly. This means that the locations of the continents have shifted considerably in the last 4 billion years.

I've included a few links where you can learn more about the crust, mantle and core. You may also want to read about continental drift and plate theory.