You put in your sig the same way you put it in a post - [.img]http://whatever.whatever/whatever.whatever[./img], without the periods in front of img.
As for shrinking it, any image editing program (even Paint) can handle that.
1. Save the image to your machine.
2. Open it with an image editor (ideally something better than Paint as that tends to slightly drop image quality, but it works if it's all you have. The GIMP is a good free one if you want something better.)
3. Save the shrunk file.
4. Upload it somewhere (use webspace if you have it, Google for a free image host if you don't.)
5. Link the image in your sig.