You can follow the following steps. Each step is meant to be realized by an algorithm, not manually:
1. Convert the regular expression to a NFA.
2. Convert the NFA to an equivalent DFA.
3. If the FSA that you have defined is a NFA, convert it to an equivalent DFA.
4. Test the two DFAs for equivalence.
Edit: There is an online implementation of the first two steps here.
For step 4 you can look at slides 2-7 here.