1) You must be 18
2) A national ID system that functions similarly to a driver's license, which is connected to your social. All citizens will be issued one at school, like picture day. There, everyone would register to vote, pick their political party and the like and get their ID. This will be provided free of charge, cost on the state and federal government will be split. Citizens who don't have one can get one from state places such as the post office, police station, DMV, etc. This is free of charge.
3) Elections are a paid national holiday
4) A standardized, national system of paper-only ballets. No digital voting at all.
5) All IDs will be scanned at the door, allowing for tracking of who voted and when. There will be no such thing as voter rolls anymore, since the national IDs will be checked against the social security database. No more needless purging of non-felons and no more dead people voting. Voting will still be secret, because this only records if you voted and when, not who you voted for.
6) On your ID, your district will be listed along with a web address of where to find your polling place. This could also be implemented via QR code.
7) This could be expanded to having your voter ID tied to a unique app on your phone, so if you lose your ID, you can still vote. Only specific election hardware would be able to read the generated code, so you don't even need your ID if you forget it. The app could also send you reminders of local/national/federal elections.
All in all, these are very simple solutions to secure elections. They'll never be done, however, because nobody in power wants voting to be easy.