|Image: Wikipedia via|
We use ancient to talk about something very old, often dating from before the fall of the Western Roman Empire:
There are ancient stones at Stonehenge.
It is very offensive to call a person ancient!
You can use old to talk about people and things:
an old man; an old building
You can also use old to talk about something that is not new:
My old computer doesn't work any more so I am going to buy a new one.
It is nicer to refer to people as elderly:
an elderly man
The term the elderly is often used as a collective noun to talk about older people as a group:
day centres for the elderly