See here for national and state level turnout rates and early voting statistics for selected states and jurisdictions, along with voting statistics for selected demographics.
The Voting and Elections Science Team (on Twitter @VEST_Team) produces the most comprehensive database of precinct boundaries and associated statewide election results. The VEST data may be accessed through the Harvard Dataverse. You can explore a visualization of the 2020 presidential data here.
Please read theFAQ for common questions on how turnout statistics are computed, data availability, and copyright permissions.