Well, first we need to answer the question: what is electricity? In general, electromagnetism is just the force that electrically charged particles exert on each other. So, you don't "create" electricity - it exists everywhere, since almost everything we interact with every day is made up of charged subatomic particles! Of course, this probably isn't what you meant: you probably meant the electricity that we use in, say, circuits (like when you plug something into an outlet). This form of electricity is caused by charged particles moving along in a conductor, like a wire.

So, the question becomes: how do we make charged particles move in a wire? Well, give them a push! It turns out that charged particles react to changing magnetic fields: if you take a loop of wire and move a magnet through it, the changing magnetic field through the loop causes a current around the loop of wire. This current can then power some electric device. In fact, this is how pretty much all of our electricity is generated: whether in coal power plants, hydroelectric dams, wind turbines, nuclear power plants, or whatever, electricity is always generated by using some power source (fire, water, wind, etc.) to rotate large coils of wire through a magnetic field. This causes a current to run through the coil, which is then carried away by power lines.