Definitely use a scanner. Scan at a high DPI, 800 or more if your scanner supports it - it will be huge but you can zoom out while you're working on it ( Ctrl and - or Ctrl and = ). Once you've scanned it in, bring it into Photoshop (I will be referring to full version Photoshop, but if you have PS Elements it might have these functions too).
If you're scanning a black and white image you may want to start with Image -> Adjustments -> Desaturate. This will remove all color information if you have a hue to the paper itself that you don't want.
Then the real improvement (also for colored pictures) will be in Layer -> New Adjustment Layer -> Curves. Click OK when it asks for a name of the layer. Here you'll have what starts off as a diagonal line going up a box. Clicking on the line will add anchor points - moving these points will either pull a range of tones closer to black or closer to white, depending on if you move it up or down. You can also grab the very ends of the line that are already there, to adjust the full scale of the tones. If you pull the top end up more, you can remove any shade the paper has completely, so that the paper is perfectly white instead of grey, and you can darken your penciling by pulling the bottom half down more, so that the lines are closer to black than to a light grey.
Play around with it, but try not to go too extreme because you will be losing intermediate shading the more you crush the tones (less shades of grey between white and black). Like anything, you must determine how far is too much.
Because this is an 'adjustment layer', it will show up as a layer; you can turn the layer off and the adjustments will disappear, or you can double-click the little circle that looks like a pokeball to open the curve box back up. This is called non-destructive editing because you can remove or edit your changes without permanently changing the pixels of your original picture. You can always go back and fix mistakes that you make with adjustment layers. Any layers below adjustment layers will receive the adjustments (unless there is a mask, but that is a different lesson!).
Now, if you have a huge picture because you scanned at very high DPI, go to File -> Save for Web and Devices. Here you'll see settings to shrink the picture down before you export to a new JPG. Adjust the percentage size under 'Image Size' until it looks like the size you want to post online. Because your picture is being shrunken, it will get much sharper and look much more clean than if you'd only scanned it at the size you wanted. When working with fine art it is almost always better to work with a big picture and shrink it than to work with the same size you will post it at.
By using File -> Save for Web and Devices, you export a new JPG at a smaller size, but you keep your original file - you didn't permanently shrink the one you were working on in Photoshop. You can save a PSD with this original file, which keeps all of your adjustment layers, so that you can go back and re-adjust your picture if you decide the one you exported was bad; you never lost data.