This Blender tutorial teaches how to make blocks that have different textures on the faces. Specifically, a grass block is made in this tutorial. This is the third video in a three part tutorial on making different materials from a single block mesh.
This is part of the Making a Minecraft Set in Blender series that may be found in the playlist below:
• Making a Minecraft Set in Blender
Another way to achieve this is to UV unwrap the mesh differently and use a single texture with all the different faces in it, but that is for another series that goes more into depth on making blocks. This is just a quick and simple introductory series.