If you want to be backwards compatible, then you "simply" do not introduce such changes, there's no "how", you don't.
A platform that works hard to be backwards compatible does only additions and extensions, and keeps maintaining the old API as well so that old apps run without changes; possibly keeping around multiple depreciated ways to do the same thing (e.g. as win32 does).
It is debatable whether backwards compatibility is worth that cost (and it often isn't), but it's certainly a choice.
A platform that works hard to be backwards compatible does only additions and extensions, and keeps maintaining the old API as well so that old apps run without changes; possibly keeping around multiple depreciated ways to do the same thing (e.g. as win32 does).
It is debatable whether backwards compatibility is worth that cost (and it often isn't), but it's certainly a choice.