I use Mozilla Firefox, and the tabbed browsing is great. One of the tabs on my homepage is the cellar, specifically I use
http://www.cellar.org/search.php?do=getdaily (which I also have saved as a bookmark/favorite) as the url for the homepage. When I launch the browser, the tabs open to the pages, including the cellar. When I see all the bold links indicating a new post, I start with the oldest first, reading the last post, using this button:

. When I've read all the posts in that thread that are new to me, I use my browser's back function, and move up the list to the next oldest unread topic and repeat the process. I may feel moved to reply, usually that's a safe bet. After I've posted my reply I use the browser's back function again until I get to the thread listing again.
When I've read all the new posts, I choose the bookmark for "Today's posts" (see url above) and then I start a new round of catching up. Rinse, repeat until it runs clear. The math geek in the house will recognize this strategy of traversing the tree and know the real name for it, but I forget what it's called.
So that's how I keep up. Toldja it was TMI.