It's easy to book yourself either online or at the counter in the old port. You will tender into the Old port of Thira. There are lots of small vendor selling boat trip tickets. We pre booked online and collected tickets from the counter. It included the speed boat to Oia and the bus ticket back to Thira. Of our group of eight, five of us did the beautiful Caldera walk back along the coastal path, about 10K, it will bring you back into the Old Town by the cable car. The grandparents got the bus. We walked down the 350 steps to the old port, as there was an estimated wait for the cable car of 90 mins. The walk down is not recommended for anyone infirm, you via with donkeys passing and it's in full sun and cobbked steps. Five people missed the ship and had to be flown to Athens to catch up, so don't delay getting the cable car down.
The following year, we got tickets at the counter for the three islands trip, it was an excellent option. First trip was about 20 euros each and the 2nd 30 euros.