Whenever electricity flows through a wire, it creates a magnetic field. In a single wire, this field is usually pretty weak. A coil, however concentrates the magnetic field. Each coil of wire contributes a small magnetic field and, together, they add up to make a much more powerful magnet.
You can also use nail polish remover to strip the enamel off of the wire, or scrape it off with a craft knife.
Decide on the core of your magnet. An iron nail or anything else cylindrical and made out of iron will concentrate and amplify the magnetic field. Some electronic coils used in tuned circuits use an air core, either winding a coil with nothing in the middle or wrapping the wire around a thin paper tube. If you want your coil to be strongly magnetic, however, you should use an iron nail or spike.
Wrap single-strand 22-gauge magnetic coil around the core. Leave about 6 inches of wire hanging off the end of the core, then wrap it all the way to the other side. The more closely spaced the coil is, the stronger the magnet will be.
Tape or glue the coil to the core. Then, cut the wire free from the spool, leaving 6 inches hanging off. You now have an electromagnet with several inches of extra wire at each end.
Strip the ends of the wires bare. One of the easiest ways to do this is to burn the last inch of enamel off each with a lighter or match. Wait a few seconds for the wire to cool, then rub the end with a clean cloth.
Attach the coil to a power source. One easy way to do this is to place the stripped wire ends under the coils of a lantern battery. The coil will now pick up paper clips and other small ferromagnetic objects.