After stumbling across a couple of tutorials I decided I would try and build my own speaker. This attempt succeeded and it surprised me at how well it actually played. This is a lot of fun and can be built for next to nothing.
It's also really great to show younger children and students to explain how speakers work. It would be ideal for a science class as there are very few components and all that can be found around the home. To assist in the learning side of it, I'll be sharing how I understand it works in the last step.

Step 1: What You'll Need:

When assembling this list bear in mind that basically all of can be improvised for e.g. the battery can be replaced by any other round cylinder of roughly the same size, depending on your cup (another item that can be replaced with other things).

- A Styrofoam/paper cup (don't try a plastic one, it won't vibrate well enough)
- A small magnet. Doesn't really matter as long as it's small, and a magnet.
- A 3.5mm headphone jack. This can be salvaged by cutting it off a broken pair of headphones or similar item.
- Some copper wire (can be attained by taking apart old TVs, stereos, but you'll probably have some lying around). It must be copper, as it is the most magnetic and conductive material that's readily available to be scrounged from around the house.

- A C or D battery/Any smallish cylinder that has a radius a cm or two smaller than the girth of your cup
- Sticky Tape and popsicle sticks (it turns out you don't really need these, so don't bother if you don't have any lying around)
- Some alligator clips. If you have some wire and a soldering iron, they'll work too for a more permanent solution, but that makes much more work.
- Something that you can plug the speaker into. I used an iPod touch just to test it, but you'll find an older stand alone radio works better as the iPod had only enough power to make the speakers whisper quiet.

Step 2: Preparing the Pieces:

FIrst, you'll want to make the copper wire into a neat circle with the two ends about 3 or 4 cm hanging off. For this, I wrapped it around a battery, then held it in place while I wrapped the two ends around the coil to hold it in shape. Once you have this coil, tape it down to the top of your cup.
Now that that's done, put your alligator clips or wire on the two ends of the copper respectively. On the other ends, put your stripped back 3.5mm headphone jack. It doesn't really matter if it's the positive or negative, as the speaker isn't polarized as far as I know.
Once this is done, tape the popsicle sticks to the cup in a way so that it provides a frame for the magnet.
Now pop the magnet on top of the frame, so it sits directly above the copper coil.
Plug it in to your radio! If it doesn't work, or it's too quiet, don't worry - just go to the next step.

Step 3: Modifications:

Now as I said earlier, mine was really quiet, and there are a couple of things I did to improve this. The first was to remove the popsicle sticks - I found it works much louder if the magnet is almost sitting on top of the coil. The second thing is to put it into a more powerful source, like a radio instead of an iPod. The third thing I did was to put a much more powerful magnet there. The tiny one I found from an old toy was replaced with a hard drive magnet I salvaged only a week or two ago, and it makes a big difference.
All of these things should give you a fully functional speaker!

Now I'm no expert, but I thought I should give a quick overview of how this works (the engineers and other hardcore hobbyists will clear this up in the comments no doubt).
The electricity being sent through the headphone jack is sent in tiny pulses that dictate how powerful each vibration will be. When these pulses are sent under a magnet, the electromagnetic field causes the copper wire coil to become a small electro magnet and vibrate as well as the cup beneath. This is why the cup is a light material such as styrofoam or paper so that it can be vibrated easily - I think most speakers use fabric rather than paper cups. As a separate project you can also experiment with a larger power source, like a 9V battery, and more coil, to create an electromagnet. Good luck!

P.S. If you like this instructable, feel free to give it a vote in the DIY Audio contest! It takes 5 seconds and it's really appreciated. Thanks!