How do I know my votes are private and that there is not a database in the computer somewhere that records how I have voted?

There is no way for the system to tie your vote to you. When you vote, there is no identifying information recorded with your vote. You will be given a randomly generated four-digit access code tied that tells the eSlate which ballot you should receive based on your precinct number. But the access code is not associated with your name. It is, therefore, impossible to trace your vote.