State Machine and State transition Table - Explanation and Creation Of
The state transition function just says "If you're in state&nbsp;$X$ and receive input&nbsp;$Y$, go to state $A_{X,Y}$", for every possible $X$ and&nbsp;$Y$.

Designing the transition function is a matter of programming; implementing it is just a case of

state := start_state
while state is not a terminating state do
    input := read_input ();
    state := A[state, input];
done