A straightforward way to represent a DFA is as a dictionary of dictionaries. For each state create a dictionary which is keyed by the letters of the alphabet and then a global dictionary which is keyed by the states. For example, the following DFA from the Wikipedia article on DFAs
To "run" a dfa against an input string drawn from the alphabet in question (after specifying the initial state and the set of accepting values) is straightforward:
state = initial
for c in s:
state = transitions[state][c]
return state in accepting
You start in the initial state, step through the string character by character, and at each step simply look up the next state. When you are done stepping through the string you simply check if the final state is in the set of accepting states.