I saw your advert in the newspaper.
I have seen your advert in the newspaper.
The OP says that he read the paper a while ago.
You use the present perfect for recent actions. So if you follow BE, you cannot use the first sentence that's in the past. Instead, you should use the second sentence that's in the present perfect.
On the other hand, you can use either the first sentence or the second sentence in AE.
However, if you are referring to times in the past or in the present, you will form sentences accordingly. For examples:
I saw your advert in the paper yesterday, last week, a while ago, etc.
I have seen your advert in the paper today, this week, etc.