1. Widespread voting in person at a number of distributed sites, with paper ballots and either hand counting or machine counting with risk limiting audits. This is pretty technologically trivial to implement, but requires manpower.
2. Widespread postal voting as it's done in places like Oregon, where there's a non-serialised ballot inside a serialised envelope. All voters are sent an envelope and ballot via postal mail, and the return can be done at either a drop box or through the postal system. On election day, all valid envelopes are opened and emptied under the watchful eyes of observers from each party. They are then counted by hand or with machines and risk limiting audits.
What should not exist are voting machines. There should always be a paper ballot in the process somewhere that is human readable.