how did the captain come by the information he gives viola about orsino?

The Captainwas bornand raised in Illyria so he knows the country is governed by a "noble Duke" (Orsino).

There are two possible answers to this question based on what the information is meant here.

The most probable information that is meant is the information about Duke Orsino being in love with Olivia. In that case, the captain came across the information through the current gossip of the people of Illyria. (Act 1, Scene 2, 7th Dialogue of the Captain)

The second meaning of the information, which, in my opinion, is unlikely, is the general information about Duke Orsino. In that case, the answer should be:

The captain was born and reared in Illyria, thus he knew about Duke Orsino.

You could write this answer to avoid confusion or mistakes:

The captain was born and raised in Illyria. Consequently, he was aware of the land where he and the others had landed. Since he was born in Illyria, he knew about Duke Orsino. He heard a current gossip from the people of Illyria about Duke Orsino being in love with Olivia. He gave that information to Viola.