The county boards of election are fun in Ohio. They're staffed by members of the two parties that took the top two slots in the last gubernatorial race. That's normally the Republicans and the Democrats although the Greens almost bounced out the Democrats due to Ed Fitzgerald being such a horrible Democrat candidate in the 2014 gubernatorial.

Typically you have to be recommended by the county party's central committee to the Ohio Secretary of State to fill any vacancy on the board. That means that you have to be involved in the local party itself and generally be a member of the local central committee. Those only get re-staffed every 2-4 years depending upon the party and generally people run for them unopposed. I cannot run for those slots for so long as I remain a federal civil servant due to Hatch Act prohibitions especially considering the nasty yet horrible agency I work for.

Structure in other states will differ. I am a former poll judge. That had to go on hold, too, for so long as I remain a federal civil servant. Once I am not a civil servant I can be reappointed relatively quickly as a poll judge.