Books are very expensive to post so I usually prefer to make a bookplate for the author to sign that I can stick into the book. This could be anything from just plain paper (which i don't do) to images of the the author with a sweet spot for signing, sized to fit in a normal envelope.

The way I've done it for 10 years has been to buy mailing bubbled envelopes from office depot or staples, take the book in one of the envelopes to the post office, have that weighed and put postage on it, then put the envelope and book in another envelope and sealed it and have that stamped to go to the signer. Books can be given a "media mail" stamp on the outside of envelope for a lower postage rate.