You register to vote, are assigned a polling place where your name will appear on a list of registered voters, and you go to that polling place and tell them your name.
If you're trying to fake it, you need to know what address and name someone else is registered at, what polling place they were assigned, and you have to hope they don't show up to vote too.
All of these uncertainties mean it's pretty difficult for an individual to do any serious (if any!) voter fraud.
Remember we had voting for a long time before magnetic strips and plastic.