But how do I get my webcam to automatically take a picture? It seems the only way to save a picture is to click on the image manually!
That depends on what kind of camera you're using, and whether the software that came with it, if any, is capable of taking automated snapshots of images. As Bob mentioned, ImageSalsa will do this for you, and ImageSalsa will also do the uploads if you wish. ImageSalsa isn't free, but worth every penny in my opinion. There may be free programs that will take snapshots as well.
Maybe someone else will chime in within the next 46 minutes with other suggestions.