You can get PC speakers designed for the job, amp built in to the speakers, for under 20 bucks, at like Best Buy:
Unless you are stuck on having the speakers you have, this will be cheaper and easier. The cheaptest you can get a new amp or reciever for, new, is about 100 bucks unless you get like a boombox.
Just about all stand-alone speakers will connect by bare wire in to those "little clicky" things, the speaker wire connector. If your speakers has plugs at the amp end of the wire they may be powered or came with some other amp / receiver.
In any event, getting powered PC speakers is likely your cheapest option and by far the easiest.
This has been asked before, generally resulting in people being told to get a 'receiver' or amplifier. The problem being i have no idea where to start looking for said things.
Amplifiers, for the most part, seem the cheaper option, however judging by the pictures some sites have shown, they don't have the correct slots to plug bookshelf speakers(literally the red and black wires that slot into little clicky things) in. Is this achieved through some form of adapter, or am i just not looking hard enough (bearing in mind i'm aiming for budget)?
The best way to answer this would be to link an example. if someone can link me all i need at a reasonably cheap price, i'll find where they live and hug them.