Paper plates are great for making simple toddler puzzles.  Below are a few suggestions.

Here is a great use for left over party paper plates with pictures on them.

Cut a picture plate into four equal pie shapes.

Give the four puzzle pieces to your toddler along with a sample of an identical plate that is still whole.

Encourage your child to put the puzzle pieces back together into a whole plate.

You will need four small paper plates in four different colors.

Cut each plate in half.

Mix up the eight halves and give them to your toddler.

Have him find matching color halves and put the four plates back together.

You will need to cut the puzzle pieces in various interlocking shapes for this activity.
Take a plate and cut it into two puzzle pieces by cutting a large pointed zig-zag line across the center of the plate.
Next try cutting a plate into three pieces using uneven edges.
Finally, if your child is successful with the first two puzzles, cut out four interlocking pieces for your child to put back together.
Hint: Picture plates can make this activity easier for your child to connect the puzzle pieces.