In other countries every citizen eligible to vote get a voting notice by mail ahead of any election.
When you then go vote to the polling place of your district/county, they have a list there of all the eligible citizens in their district/county, you'd have to show the voting notice you got and some ID, and they'll let you vote crossing your name off a list.
Voter IDs are for protecting a citizen's right – otherwise every, say, tourist could participate …