Theory of Computing
THE HYPERTEXTBOOK
Chapter 2. Finite State Automata, Regular Languages, Regular Expressions, and Regular Grammars
Section 2. Finite State Automata

Example

Are all FSA's as simple as the first two demonstrated in this section?  No.  They are pretty wimpy, but they certainly can solve more complex problems than the even and odd parity FSAs.  Here is one with a bit more complexity.  It accepts all strings that contain either a 101 or a 010.  Give it a try.