How to complement a dish?
You could certainly get a cookbook of side dishes and learn some new favourites, but what might be more useful is a book that teaches you about flavour combinations and menu planning.  I would suggest Culinary Artistry as one such book.  It's not about specific recipes (you can find those elsewhere or make them up), but rather it addresses the kind of skill you're looking to learn.

One technique is to consider the origin of the main dish and choose side dishes from the same region.  Seasonality or market-based shopping is another approach to expanding your repertoire.