In Australia we go to polling booths to vote.
Our polling booths are
in the polling stations.
A polling station is typically a large room, perhaps in a church hall, school, or community centre.
At the polling station there is a reception desk (or perhaps several) where you show your polling card (not an absolute requirement, but it makes the process quicker -- alternatively you can just tell them your name and address and show some ID). Your name is then crossed off a list (so that you don't vote more than once), and you are given a ballot paper and directed to the polling booths of which there might be a dozen, where you vote by placing crosses in boxes on the ballot paper using --you guessed it-- a pencil. Then you'd return to the desk an put your paper in the ballot box.
The pencil used to be tied on with a bit of string, but the last time I voted, it was as we were coming out of the depths of Covidmania, and this pencil was considered a risk: a vehicle by which voters who might be infected could spread the disease to others, so we were
given a pencil at the desk, which we could then keep. They were small, like the ones you get at IKEA. This was all a bit silly, since you'd be touching the writing surface in the booth anyway.