Square wooden blocks
Lots of scrapbook paper
Medium/fine and fine grit sand paper
Optional: Paint or wood stain
I have seen baby blocks like these for sale for more than $20 for sets of 6-9. Every time I see them I think, "Awwwww!" and then I think, "I could do that!" I'm sure you can, too.
Step 1: Sand the blocks
Sand the corners of the blocks with medium/fine-grit paper until they are nice and soft and you wouldn't mind your little kiddo handling them. Give the faces of the blocks a little rub, too, to get the store-bought feel off (and maybe the sticky stuff from the price tags).
At this point, you can paint or stain the blocks to give them a different look. Let them dry for at least several hours before continuing.