You start with the initial states, maybe there is only one or two. Then, you consider the transition relation where the state variables have been replaced with the constants that determine the initial state that you consider. Then, you compute the satisfying assignments of the specialized transition relation which enumerates the transitions from that initial state. That gives you further states that are reachable, and you have to proceed next the same way with them.
Proceeding this way will make sure that you will not waste time for computing transitions of unreachable states.