What is the procedure for reproducing, in one's book, a photo that is in the public domain and found online?

I'm not an expert.  But I do know it's a minefield.  Public domain is a legal status, and is not the same as being publicly accessible.  Finding something on the internet is no guarantee of any kind.  If you want to reproduce any work by anyone with the intention of enhancing your own work, it's worth your trouble to track down the original publisher and/or copyright owner, and getting formal approval.  If you don't, you could end up paying through the nose.

Thanks Jo. Don't want to pay through the nose. I will forego anything that is not from the home-grown photos given to me with permission--cows, barns and butterheads mostly.

I think that's the safest option.  Full marks for thinking about it before committing yourself!  Good luck with the book.