If there is a curfew from 8 PM, how does on go to mikveh if the time of tvilah is after then?

One can go the following day during the day, but not the day of the tevila during the day (see shulchan aruch 197, 4).

If this is not possible, there are opinions that allow one to go to mikva even the day of tevila (as late in the day as possible) as long as she doesn’t return home until after nightfall (see sidrei tahara s.k. 9). If there is a way to arrange this, curfew permitting, in a time of need one can rely on these opinions (see Igrot moshe Y.D. vol 3 60, Taharat Habayit 14, 5). One should consult a rav as to how such an arrangement should be made.