Which restaurants?
Fifteen minutes before your reservation time is about the earliest Disney recommends. Depending on the restaurant and how busy they are at the time you arrive will determine whether you'll be seated early, still have to wait until your reservation time, running behind and have to wait past the res time, or are asked to come back closer to the res time. There's no hard and fast answer.
As far as how late you can be, it will depend on the restaurant. Disney does not have an official grace period policy so while most restaurants will give you about 15 minutes that is not guaranteed so as much as possible plan to arrive on time. We were waiting at a restaurant running behind schedule that didn't have a grace period one evening and turned away anyone who arrived after their reservation time.