Three-phase pattern for schema changes: add the new column, dual-write to both, backfill in batches, switch reads, drop the old column. Each phase is independently deployable.
For huge tables, use a tool like pt-online-schema-change (MySQL) or pg_repack (Postgres). Default ALTER TABLE on a big table locks for the duration.
The trickiest part is dual-writing — application code must be careful which column it reads while the migration is mid-flight.