For in person voting, ID must be shown, the signature pad signed, to receive a ballot. As Jim said, the paper ballots are marked and then fed into the tabulator by the voter.
For absentee voting, a ballot must be requested by the voter, and when received, it must match up to not only the name on the voter roll, but also the signature on file.
Florida started counting absentee ballots weeks ago, so when the polls closed on Tuesday those votes had already been entered into the system.
I voted in person, the 2nd day after early voting began on October 19th.