OK, here's the super-quick n' dirty method I've been using. There are probably easier and better ways that I'll discover if I spend more than 90 minutes trying things out, or if I actually do some research. I used Photoshop & Illustrator quite a bit a few years ago, but I'm rusty and out of practice.
Short Version: make it b&w; select the part you want; invert; delete; trim; erase big bits; select by color range (highlights); delete; erase anything left over; save as png.
1. Get a clean jpg. I'm not even bothering with colored stuff. b&w/greyscale or nothing. If I have a pdf, either select to copy or use the clipping tool in Windows to cut it out. I'm sure you could do it in Photoshop; I didn't bother. If the jpg is greyscale, I usually bring them into Picasa and click the "I'm feeling Lucky" button. Again, you can do this in Photoshop and I might from now on, but Picasa is nice if you're doing a bunch of stuff and not used to a Photoshop workflow (I'm way out of practice).
2. Assuming you've got a decent jpg of the page, like the ones from Wikipedia, bring it into Photoshop. Make a duplicate layer and hide the locked background layer.
2a. I made my transparency light pink (Edit -> Preferences -> Transparency) rather than b&w checked, because b&w stood out a lot better against it.
3. Select the part of the page or image that you want. I use the rectangular selection because it's fast and easy.
4. Invert the selection. (Shift+Ctrl+I)
5. Press delete. Everything outside of the selection should disappear, showing the transparency (if you've hidden the bottom layer!) Ctrl+D deselects. Now you'll have a little image and a lot of transparency.
6. Go to Image -> Trim and select transparency. All the transparency will go away, just leaving the selection.
7. Ctrl+0 fits the image into the screen (because it's probably kinda small now). I like to get out the eraser at this point and go around the edges erasing the obvious stuff, like cut-off words and crummy borders.
8. Go to Select -> Color Range and from the drop down menu select Highlights. It should select the lightest parts of the image. Press Delete. Deselect again. If you didn't erase the stray stuff around the edges, you'll have to do it now.
9. Trim again. Depending on how tight your initial selection was, it might not come in at all, but if you've got a large margin of transparency that won't go away, then there's hard to see stuff in there. Get out the eraser and zip it around again. If you want to SEE what you're erasing, make a duplicate layer of this one, move it below, select all, delete all, and then fill all with black. That will show up any light greys or whites that you can't see against the normal screen color. Just remember you have to go back to your working layer to actually erase those.
Remember, in most cases this will be against a white background. If there are some stray white pixels in there, it's really not going to matter.
10. Save As -> PNG You lose transparency if you save as a jpg or flatten the image, I think.
Extra stuff: I made multiple copies of the base jpg file and labelled them right in Windows, and then edited each one in Photoshop. There is probably a way to do it in Photoshop (1 file -> multiple copies & edits), but I didn't want to bother remembering it or looking it up.
Extra Extra: If you're making a vignette out of a larger scene, like my bottom two images, you'll have to spend more time with the eraser to delete lines and get it looking how you want. I'm picking areas that are easy to break out anyways, so it's really not a big deal.