Wick is not the centre of the world - and its connections with the rest of Britain prove that quite well. Wick sees only limited bus and coach service and also train services aren't the best either. If you rely on public transport, it is the most obvious choice anyway, especially if coming from Invernness or Thurso. There are four trains daily (MON-SAT) on the route Inverness-Thurso-Wick. It takes a little more than four hours for the whole route.
For fares and timetables check the National Rail page or one of the usual pages like thetrainline.com.
If you would like to save time on your way to Wick instead of taking the train via Inverness, you may consider flying into Wick. The town has a small airport which links it with Edinburgh, Newcastle and Aberdeen. Especially the flights to Edinburgh, which are operated by FlyBe, can be a bargain when you book in advance.
There is no public transport from Wick Airport into the city centre. If you have a lot of luggage with you, you can order a Taxi. However, the airport is just a 20 minute walk from the city centre away.
Keep in mind that the airport building is closed until two hours before each departure. The small shop which sells drinks, snacks and souvenirs is not open regularly.