Peter,
to put it in Black and White: Well = a state you are in. You are feeling well. How are you? I'm well. (Although..... people have started to say "i'm good', which originally means "braaf").
When a word refers to a verb you add -ly. As Linda said: he speaks softly. Softly refers to the
verb, hence the added -ly.
Look at the difference : the pillow is soft. 'Soft' refers to a
noun. So no added -ly.
More examples:
That is a beautiful room.
She has done up the room beautifully.
He is a mysterious guy - 'mysterious' refers to a noun (guy)
He has mysteriously disappeared. - 'mysteriously' refers to a verb (disappeared)
Of course there are exceptions to the rule, to keep us alert
By the way, an adverb is a 'bijwoord'. Don't mix that up with a pronoun (bijvoegelijk voornaamwoord).
If you see a discriptive word, then wonder what is it that is says something about; is it about a THING, or is it about a VERB. There you go, that's the difference. If about a VERB, then add -ly.
I hope I make sense