* Add the new schema
* Write to both the new and old schemas, keep reading from the old one (can be combined with the previous step if you're using something like Flyway)
* Backfill the new schema; if there are conflicts, prefer the data from the old schema
* Keep writing to both schemas, but switch to reading from the new one (can often be combined with the previous step)
* Stop writing to the old schema
* Remove the old schema
Leave out any one of those steps and you can hit situations where it's possible to lose data that's written while the new code is rolling out. Though again, it depends on the change; if you're, say, dropping a column that no client ever reads or writes, obviously it gets simpler.