Use paper ballots. Scan them at the polling place for fast electronic tally.
Audit a significantly significant random sample of the paper ballots after the election, and do a full recount if any discrepancy is found.
Prosecute people that violate chain of custody for the ballot boxes. (Give this power to a non-partisan authority.)
There are open problems around tampering with voter rolls; this is done both by state governments and foreign powers. We still need a scheme to make this more detectable (and to invalidate the election when it happens).