Several companies offer these tours. Many of them have stands on the beach promenade in Hvar, check the prices and what is included before you book.
We chose a whole day trip including a stop in Komiza on Vis (see my Komiza page) and a short swimming stop by the Stiniva cove. The picture shows Stiniva seen from the sea, ChristaV has a picture of the cove seen from inside and kia81 has one seen from above.
The Blue Grotto was great, I have written about it on my Bisevo page, including a travelogue with 8 pictures. The only negative thing about it was that there were many visitors and only a short period to visit: The light conditions are best around noon. Thus we had to wait quite long for our turn, and the visit was short.
On the return we were served a delicious lunch which (off course!) consisted of local fish.
We did a day trip to Vis, and it was one of the better decisions that we took whilst on the island, although I must admitt we made a few good decisions.
Vis was a military island and closed to the public for long, when you visit it, you get the feeling that nothing has changed there in the past few hundred years.
We pulled into this little cove, as part of our day trip to Vis Island. It did look so fantastic and idyllic. I am not sure if anyone actually lives in the house or if it is a weekend getaway place. It just looks idylic.
You must take a day outing to Vis island. This will allow you to visit the green and blue grotto's. We were lucky and had a singing duo on our trip, so they used the accustics of the green grotto and serenaded for us. What a wonderfull experience. The blue grotto is not as difficult to enter as the one in Capri, Italy, but equally stunning.