Usually they are offering some sort of prize (random number pick) for someone who comments on all the blogs. Sometimes they require that you become a Follower of the blogs. On one that is sponsored by a stamp company, the owner or designee will start the blog and they list everyone else's links to their blog so you can follow them. Also on each blog they will give you a link to the next blog. Basically, you just hop from blog to blog and leave a comment. I've found that some of them will come back and post on my blog.
Another way to get blog followers and comments is to take part in the different challenges. I made up a challenge list last night. I'll post a copy here in case your're interested. When you take part in a challenge and post your card on their website, then you can get traffic from that post also.