My town has six districts for the village board but we only have one polling place for the whole town (it’s a small town) additionally you can vote early at the county office.

They simply print your ballot when you give them your name at the polling place. You fill in the bubbles and then put it into the ballot machine. It counts it electronically, but it drops down into a locked cabinet.

I’m assuming it’s the same procedure for everyone in my county for all the different voting/government body districts people are in.