If you don't have a car bus is the way to Kuldiga. There are good links to Riga, Liepaja and Ventspils. The main bus station (Autoosta) is about a 15 minute walk from the centre, it's easier to buy tickets here if you don't speak any Latvian, most buses do stop closer to the centre on Mucenieku iela.
Tickets are cheap and the buses are reasonably new, sometimes small though.
Kuldīga's bus station (auto osta) is quite far from the town centre, at Stacijas 2.
As you can see on the picture, all you see from there is green, scattered houses and also an abandoned factory, quite a desolating view! But don't worry, you can go to the town centre in 15 minutes of walk, a bit more to arrive to the 2 main hotels in town.
There are buses to/from Liepaja, Ventspils and Riga every day, as well as to/from smaller towns there around.