Can you alter the charge on an electromagnet?

There are basically two types of electromagnets,

one runs on DC current: on a battery for example;

and one runs on AC current, like what you get from a household electrical socket.

The ones that run on DC current have a clear north and south pole, and if you reverse the polarity of the current - if you simply switch the wires coming from the battery - you will reverse the polarity of the electromagnet.

Electromagnets that run on AC rely on a core that is able to change polarity very quickly, and they actually change polarity 50 or 60 times a second, depending on your AC supply. For this kind of electromagnet, neither end is either north or south for long, so reversing them would not have much meaning.

Yes, there are switches which will reverse the direction of the current flowing through the electromagnet's coil. School science supplies companies would have them in stock. Here's a link http://www.kpsec.freeuk.com/components/switch.htm which shows how to connect a reversing switch.

By "charge" do you mean the strength of the magnet? That is controlled by how much current is flowing through it. If you had a voltage controller of some sort that let you vary the voltage, that would do it.

Commercial electromagnet coils are called "solenoids". You might want to search that word if you're looking to buy one.