How do I take a crappy scan like this and turn it into a clean image?
The full explanation is below. I use Photoshop, but most of this applies to other programs as well, even if the commands are different.

Yuck! This is what you get when you scan at 300dpi grayscale. It beats black and white, but it takes some cleaning up first. Go to [IMAGE->ADJUST-> CURVES] and make a curve like the one below.

Twiddle your curve until the whites in your image are white, the blacks are black, and you don't start to lose your lighter lines. Don't worry if there are still marks on the image. When you're done with the curves, choose the Dodge tool (it looks like a black lollipop). Set it to Highlights, 100%. Find a nice brush size and use it to clear up eraser marks and such. Then change it to the Burn tool, and set it to Shadows, 100%. Use this to darken any light lines.
Next, choose [FILTERS->PIXELLATE->FACET]. This gets rid of annpoying little dots. Set the foreground color to black and choose [SELECT->COLOR RANGE]. See below:

Set it to Sampled Colors, Fuzziness=200, and press okay. Then choose [SELECT->MODIFY->EXPAND]. Set it to 1 pixel.

Now you have all the darks selected. Go to the Paths palette, and open the palette options menu. Select MAKE WORK PATH. This will turn your selection into a path. It may take a little while. Now, choose [SELECT->ALL], and press delete. You have just deleted the whole image. Don't panic. It'll come back. Go back to the paths palette, and the palette options menu. Select your work path. The image should look like this:

Choose FILL PATH. Fill it with black. Then drop the work path into the little trash icon. You may want to touch up your image a bit more, but it should look something like this:

Voila! The finished product!

Note that in Photoshop, you can drastically speed things up in the future by recording most of this (From the FACET filter to trashing your Work Path) as a single automated action that can be triggered with the push of an F-key.

Now you just have to reduce the size of the file. Go to [IMAGE->IMAGE SIZE] and change the resolution to 72dpi.

If you prefer to save your file as a JPEG, I find the 40-50% quality range gives pretty good compression with little to no loss in quality.

If you want to go smaller, save as a GIF. Go to [FILE->SAVE FOR WEB], set it to Web colors, number of colors to Auto (It should reduce to six), and no dithering. GIF gets you very good compression but if you color your images, steer clear.

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