> Like, do I need to know how the routing works, in MVC?

Not if you use attribute routing. It's one (probably the main) advantage. e.g.:

    [RoutePrefix("api/chat")]
    public class MyChatController : ApiController
    {
        [HttpGet]
        [Route("/greeting")]
        public HttpResponseMessage SayHello ()
        {
            return Request.CreateResponse(HttpStatusCode.OK, "Hello World");
        }
        [HttpGet]
        [Route("/farewell")]
        public HttpResponseMessage GoodBye()
        {
            return Request.CreateResponse(HttpStatusCode.OK, "See you later");
        }
    }

So the routing is controlled solely by the RoutePrefix and Route attributes rather than the method names: e.g:

http://mysite.com/api/chat/greeting