RESTful Web APIs

this this this this this this I cannot recommend this book enough. Read it, read it again, take in everything it is trying to say and try as hard as you can to understand it. There is a whole world of awesome and tragically misunderstood tools in the book.

I think it depends on what type of API you'd like to design. If you're talking about REST APIs, then the best book I've come across is RESTful Web APIs by Leonard Richardson and Mike Amundsen: http://restfulwebapis.org/ It actually shows you how to do REST properly, not that shoddy knock-off REST that some people push, where you have to document all your URI structures and hard-code them in your clients. There's solid examples that you build upon throughout each chapter, and jumping off points to standardisation work like JSON-LD etc.