Algorithms for logical synthesis
This is an instance of logic synthesis.  A standard approach is to use Karnaugh maps or the Quine-McCluskey algorithm.  Finding the minimal circuit is hard (see circuit minimization), but there are tools and techniques that often work reasonably well in practice.  For instance, you can use the Espresso tool to help with this; there are other tools for this task as well.

See also Creating a logical circuit and Working out the connectives (And, Or, Not) in a Truth Table that has the outputs.