how does mutation and adaption fit into the evolutionary process?

Answer 1

Mutations cause variations in the population. If a mutation helps an animal survive in the environment, then it will survive and have offspring. The offspring will also carry the mutation and that is an "adaptation".

That is the basic idea, but you should really read more in-depth into the issue so that you fully understand evolution. Too many people these days are unaware of the subtleties of evolution and have the wrong idea.

Answer 2

Mutations of DNA can be either "spontaneous" (ie. they can happen randomly at any time) or as a result of external influences (radiation, chemical exposure for example). All offspring within a species have variation of their DNA due to these mutations, and many other variation factors including cross-over. Within a species the organisms that live and survive to reproduce have traits that are "adaptable" to their current environment, so the passing of these adaptable traits from generation to generation is adaption. The traits that are passed are not all necessarily mutations, but random mutation enhances variation of traits!

Answer 3

Adaptation is evolution and mutation is just a bad combination of genes. Of course, evolution/survival of the fittest clears mutation right up.