I was Googling Babylon 5.
I first came across the Straight Dope in a book store. Bought it and noticed several mentions of AOL. Some time after that, I got a computer, got online, and got on AOL and found the SD forum.
The TV Show. Yes, I am that old.
By the way, does anyone else want to drag every one-off poster whose only post is a “boo hoo, here’s my incredibly tragic, Jerry Springer story that I need advice on” OP and make them answer the question?
I submitted a question for Cecil via internet. The response was Cecil is very busy. But you could submit it to the geniuses here for an answer. I did. Got my answer and got hooked.
Via a link, or a reference, on another message board. It was only a year ago, but I can’t remember which !
Google. I was searching for something relatively obscure, and found a link to a discussion about it. I have no idea what the actual search was, though. Possibly something to do with physics.
I used the print Reader for a long time while living in the Chicago suburbs in the 90’s. When I scored my Chicago apartment in 2000, I used the Reader Classifieds online because they posted the apartment listings the nigh before the print paper came out. From there, I started using the online Reader and the Dope, and discovered the Boards through Threadspotting. I was briefly a member in 2001, I think, then lost my way and forgot both my old username and email from back then when I joined again in 2007.
Other: Via an announcement in the alt.fan.cecil-adams USENET group.
I was looking for an internet forum with deeper discussions than most offer.
Still looking… 
I found the online archive of Straight Dope columns. I’ve never seen the actual newspaper.
There was an…issue with a religion-based message board long ago (apparently 14 years or so!). I came over from there to see what people were talking about. I ended up staying here and giving up on that one.
Someone made a comment about the SDMB on Snopes. I came over to check it out and never looked back.
Me too. And I’m irked that this option is always missing from the perennial polls on this topic.
I voted “some other way” because it happened like this. I started reading the column in the Baltimore City Paper in the late 70s. I bought the first book when it came out, and bought at least one more. I continued reading the column in the paper. In late 2000, I moved from Baltimore to Chillicothe, OH and started a new job in Columbus. After a few months, I did a web search in the hope of finding a local newspaper that carried the column. I found the web site, which eliminated my need for a print version.
I noticed the Threadspotting link, clicked on it, and became a dedicated lurker in early 2001. It took me until June of 2005 to join.
I still haven’t found the place, sorry.
But really, I think it was a link from a previous search engine. I read the front page columns for a long time before I looked at the forums, and I read the forums for a long time before I registered.
That’s the first I knew of Straight Dope too.
Found a link on a car enthusiast board.
Killing productive time ever since.
Other: Print weekly column (same source as Crotalus, c. 1980), to books, to alt.fan.cecil-adams (ah, USENET…) circa '94, to website once it was out from under AOL. So I cannot strictly say I was led here directly from the column but neither did I come here fresh from e-space sources only.
If by “Google” you mean “Lycos,” then “Infoseek.”
I found Straightdope.com through some web search in about 2001 and was a religious follower of new columns, and avid miner of the archive, for five full years before I thought to join the forum.