If you are driving from Inverness, take the A9 northbound to Thurso. Then take the A882 to Scrabster and catch the ferry to Stromness. From there, take the A965 to Kirkwall.
If you are coming from Aberdeen, take the A96 to Inverurie, then the A920 and A96 to Nairn. From there, take the A9 northbound to Thurso, then take the A882 to Scrabster and catch the ferry to Stromness. From there, take the A965 to Kirkwall.
If you are coming from Lerwick in the Shetland Islands, you can catch a ferry to Kirkwall directly.
If you prefer to travel by train, the nearest train station is in Thurso. From there, you can take the bus or drive to Scrabster and catch the ferry to Stromness. From Stromness, take the A965 to Kirkwall.
Alternatively, if you are travelling from Glasgow or Edinburgh, you can take a train to Inverness and then follow the driving directions above.
When travelling to Kirkwall, it is worth leaving some extra time to explore some of the other fascinating sites on the Orkney Islands, such as the Standing Stones of Stenness or the Ring of Brodgar.