Anyone who doesn’t already have it set up that way: you can set it up that way by going to User CP, clicking Edit Options, and looking under Default Thread Subscription Mode.
I use http://boards.straightdope.com/sdmb/usercp.php as my bookmark bar button, then New Posts.
I’m automatically subscribed to anything I post in.
I scroll through the topics, and middle click for a new tab. Sometimes I pick out more than one, but usually it’s just one thread. I use new tabs so that all the threads I haven’t seen stay bolded, and I keep my place in the list.
Occasionally I will write a reply before reading the entire thread, so I don’t forget–and I delete it if I don’t think it adds anything. And sometimes I write something in a tab and leave it open, debating whether I should actually say anything. And so I go do something else. Other times, I know I have something to say, so I open a reply tab, but leave it there and do something else until I have a good way of saying it.
Using New Posts is not appealing to me, as it jumbles everything up into one stream. (It’s why I don’t use an RSS reader or subscribe to people on Twitter. I don’t see the point.) I also do not generally subscribe to posts, nor go back and read to keep up with them. I say what I want to say, and I come back later if I’m interested later.
Only when I’ve asked for an answer that is important to me do I subscribe. Most often, these are my actual threads instead of posts, since I don’t tend to start a thread unless I want to know something.
I go first to the Game Room, since I run the Death Pool. Then MPSIMS and Cafe Society. I never go to Great Debates, or almost never, and the Election forum is unknown territory. I dip into the Pit maybe every third visit. My last forum is usually IMHO.
I’m approaching 70 years old, and not a “natural” with computers. My dealings with navigating the Dope, are just as per the above quotes: I strongly feel, rightly or wrongly, that trying to get to grips with whatever “clever” procedures / short-cuts – would for me sort out worse. than continuing to do it the cumbersome way which works for me, for the roughly half-dozen forums on which I spend a significant amount of time.
I just work backwards through the threads with new posts, up until recently, anyway. I’ve lost interest in Elections…too much effort for not much ignorance fought. 
But since football season has started, I’m in The Game Room a lot and still check the Café Society and IMHO sections…and a couple in Thread Games.
I’m auto-subscribed (no emails) and so click User CP first. When I’ve gone through those, then New Posts.
Now I understand why people sometimes say, ‘‘Sorry, I didn’t realize I wasn’t in the Pit’’ and other such things.
nm
Apparently, the Advanced Search remembers the amount of time that you like searching. At some point, I set it to “Newer than 2 weeks”.
I either browse around looking for interesting threads, or I go into Advanced Search, put my name in, and hit Search. It will pull up all the threads I’ve posted to in the last 2 weeks.
I’ve never looked for the Subscribe button, though I was aware it exists. I’m not keen on having ancient threads come up. The 2 weeks approach works well. Though, I do wonder if it is more or less efficient for the SDMB’s database than the subscription search. I suspect it’s about the same.
I search my name to see if there have been responses to threads I’ve participated in, then I check the forums I use most to see if anything interesting is going on, or revisit threads I haven’t posted in but am following.
I don’t subscribe or use the “New Posts” button, I just wing it and hope to stumble on things as I scan. I have probably missed out on a lot of cool stuff, but them’s the breaks. There’s only so much SDMB I can consume, anyway.
I hope that if I’m ever singled out for anything in particular in a thread, be it praise or pit, somebody will PM me to tell me. So far that hasn’t really happened, seventeen years and counting.
The way I use the board, it’s easy to lose track of which forum you’re in. But I can usually tell by the context and tone of the posts. If I post, however, I’ll double-check to make sure my response is appropriate.