In reply to Dangerous Dave:
To get to the Orkneys, you can take cars from Scrabster to Stromness, or go on foot(*).
To get from Mainland Orkney to Hoy there is a tiny passenger ferry from Stromness to Moaness, or a vehicle ferry from Houton to Lyness.
I think most people probably do it on foot. If you are happy pre-booking a taxi on Hoy, or enjoying the beautiful cross-country walk to Rackwick instead, then there is no real need to bring a car to the Orkneys. I second Tom Last's comment about pre-booking. Moaness is basically a pier and a couple of crofts - there won't be a taxi rank waiting for you!
(*) If leaving Scrabster as a foot passenger, be warned that it's a little walk from car park to ferry jetty, foot passengers must check in 30 mins in advance, and the ferry has been known to leave early if all checked-in passengers are on board. Yes, I speak from experience here!
Post edited at 17:56