I've noticed some sites have a small graphic by their domain name http://www.artofapproaching.com/ (that is also saved by the bookmark)...how do you get one of those?
That's called a favicon, you need to have one first (it's an image in a .ico format) and then put a piece of code in the header of your html and you're done. If you search for "favicon" here in the forums or using any search engine, you'll find plenty of data, don't worry.
Actually you don't need to put the code in the HEAD section of your Web page. Just drop it in the root folder of your Web site and the browser will pick it up when the server sends it with the rest of the Web page.
It should be in the root directory though. If you look at your server logs, you'll notice a bunch of 404 errors for the /favicon.ico file if it's not in the root folder. Avoiding those false positives (same with the lack of a robots.txt file there as well) is a wonderful thing for those of us who actually look at our server logs on a regular basis (which should be everyone who has reasonable access to them).