1. Get a jpg of the image that is as high quality as you can possibly find. This image really needs to have very few solid colors. Two-color is great, gradients are awful.
2. Download and install Inkscape http://inkscape.org/download/?lang=en
3. Open Inkscape
4. Click File > Import..., choose your image and click Open, make sure "embed" is selected and click OK
5. Click the blank white area of the canvas to de-select the image. Click the image to select it. Click the image again to make the borders change into rotation mode. Click it once more to go back to resize mode. Hold Control while resizing or rotating to have it snap to reasonable values. Now you know how to manipulate basic objects. In the toolbar on the left, the topmost arrow will make this your tool. Ctrl-Z when you're done playing around.
THE GOOD STUFF
6. With the image selected in the resize mode, click Path (in the top toolbar) > Trace Bitmap
7. In the Mode tab, fiddle around with the settings until you can produce a good vector. If I have a 2-color image, I usually choose Color quantization and set Colors to 2, or Colors with Scans of 2. Hitting Update will show you a preview. Hitting OK will generate one vector image group layered on top of your image.
8. After hitting OK, drag the vector image off of your image so we can work with it separately.
9. Double-click the image to dive into it's object. The object you are currently editing is displayed in the bottom left as a dropdown box. When no object is selected, it says "Layer 1".
10. When inside an object, try dragging the parts of the image out. If you scan multiple colors, you may find that another color matches what you were looking for better than the color you thought you wanted. Some of the outputs leave a background, and you will want to remove this before laser cutting.
11. Once you've identified a good auto-vectorized trace-bitmap'd layer to work with, close the Trace Bitmap window, delete the original image from your workspace (double-click the background if you want to get back to Layer 1), and double-click the layer you want to work with. This will enter the "Edit Paths By Node" tool, which is the second from the top in the left-most toolbar.
12. Control + scroll wheel will zoom in and out towards where your cursor is, Control + left click drag will let you drag the viewing around around the image.
13. Drag the control points around to make the image look more like what you want. You can select and delete control points, drag the curves between points, and change the behavior ofpoints with the point-modifying tools in the upper left under the file menu. Double-clicking on a line will add a new point.
And that's about it! Post whatever you come up with and we can give you some more help
. Let us know when you'll be at the lab so we can help you in person. I must stop avoiding work now, ttyl!