There are lots of ways you can make a simple electric motor. Lots of them do not work. The best one I have found is called “Beakman Motor”, name after the character on Bill Nye. One good example of how to build it is at http://sci-toys.com/scitoys/scitoys/electro/electro.html#motor
Search the internet for images and plans for the Beakman Motor and that will help you design your own. Keep a couple of tricks in mind:
a) Use a regular battery holder, like you can buy at Radio Shack. Using a board with nails (see the picture) often leads to failure and nothing dampens a science activity with kids like one that does not work.
b) Pay real attention to stripping the wire. Wire is coated with either enamel or plastic, and it won’t conduct electricity until the coating is removed. In many of these Beakmans, the end of the coil (called the “armature) have the coating removed on one side but not the other. That is critical to making it work.
c) Use a larger battery. Whether you pick a D, C, or even AAA they all have the same voltage; about 1.5 volts. What you need is more current, which is not the same. The D and C cells provide more current. Be aware, these little motors do eat through batteries in a hurry. Have fun!