How do blogrolls work, and how do I get on them? Is it usually a link trade, purchase, or just someone including blogs they like?

Any and all of the choices you mention. At the beginning a blogger will often add links to other blogs he/she admires without expecting anything in return. That is what I did. As several of those blogs noticed me and the quality traffic I was sending they added me to their blog roll.

Another blogger that I was commenting on emailed me and offered to do a reciprocal link for a link exchange. That has been successful for both of us.

The really popular blogs don't seem to do blogrolls. I guess they figure that they don't need to endorse other sites on a blogroll but they tend to mention other blog posts within their posts which drive lots of traffic.

To get on other peoples blogrolls:
1. Produce killer content
2. Comment a lot on other blogs with insightful comments
3. Become an authority in your niche and others will start endorsing you with their blogrolls and links in their posts.

Good luck,