An algorithm to compute a set of states that satisfy a specific CTL formula
The set of states satisfying $\exists a U b$ is the smallest set $S$ such that


$S$ contains all states satisfying $b$, and
$S$ contains all states satisfying $a$ which have a successor in $S$


Note that we specify the "smallest" such set because otherwise you could  pick the set of all states, or include arbitrary cycles of $a$-states, etc. Do you see how to get an algorithm from this?