Reddit reviews Baseball: A Film by Ken Burns (Includes The Tenth Inning)

(1) Read, bruh. I can't vouch for it personally, but I've heard the book Watching Baseball Smarter recommended with high regard. And it's almost literally the exact thing you asked for. Here are some other good book recommendations:

• Moneyball by Michael Lewis. Hard to believe that the book is sort of old hat at this point, but it still serves as a very readable introduction to advanced statistics.
  
  
• The New Bill James Historical Baseball Abstract by Bill James (mostly). This book is good toilet reading, if you have a massive toilet on which to perch it, and your bowel movements are glacially paced. James ranks the best players at each position, and goes on a witty, decade-by-decade jog through the history of the game.
  
  
• The Book: Playing the Percentages in Baseball by Tom Tango. Are you a "math person"? Read this book, you'll like it. It's an introduction to sabermetrics that explains the important first principles of statistical analysis, builds an important statistic (wOBA) from the ground up, and then applies all of that knowledge to answer specific questions about baseball strategies and to debunk, verify, or qualify some of baseball's hoary "conventional wisdom."
  
  
• The Amazing Adventures of Kavalier and Clay by Michael Chabon. This book is not about baseball, but it's still great and you should read it.
  
  (2) You'll want to start watching the game more, if you can. Find a method (like MLB.tv or, you know, your television) to do so. Massive exposure does help you learn, and it's a fun, if inefficient, method. Osmosis. That's just science.
  
  (2b) Depending on the broadcast crew, it's sometimes addition-by-subtraction to mute the television.
  
  (2c) If you have MLB.tv Premium and intend to follow your favorite team, I recommend watching the other team's broadcast. You know enough about [TEAM X] already. Learn something new about [TEAM Y], instead. Unless, of course, (2b) applies, in which case maybe your best bet is MLB.tv's option to overlay the radio broadcast on the TV video. Barring that, the liberal application of the DOWN VOLUME button is always an option, and then, like, listen to Chopin's Preludes. Don't be That Guy and lean too heavily on No. 15, though. There are 23 others. Expand your horizons.
  
  (3) When you go to games, keep score. Sure, there's a guy a few seats over in a striped button-down and pre-faded jeans (Chad or something) who will mock you mercilessly for it. Sad for you, you've lost Chad's respect. But, oh, the things you'll gain. A free souvenir. A better grasp on the flow of the game. The priceless power to answer the "what did I miss" and "what the fuck just happened" questions that litter the air at ballgames, tragically disregarded and forgotten like the syllabi from Chad's last semester at Bromaha State. You can learn how to score ballgames here. Fuck Chad.
  
  (3b) Go to games alone now and then. Did I mention that, in some company, it's rightly considered rude to score a ballgame like a trainspotting anorak? Not in all company, mind you. But I like going to some games alone to avoid the messy politics of divided attention altogether.
  
  (4) Bookmark a few websites. Quick stat references include FanGraphs, Baseball-Reference, and Brooks Baseball. Grantland, Baseball Prospectus, Baseball America, and the Hardball Times are all good. FanGraphs and Baseball-Reference both have subscription options that allow you to access enhanced content for a small fee, which is worth it if only to support the yeoman's work that they do compiling and sorting our beloved numbers.
  
  (5) German chess great Emanuel Lasker is believed (incorrectly) to have said that "if you see a good move, look for a better one." Good advice. Too much of the history of baseball analysis is the history of people getting stuck in comfortable places and refusing to interrogate their own ideas about the game. Sabermetricians have made careers out of just pointing this out, and even some of them do it from time to time. Also, on the level of pure self-interest, baseball ignorance and bad teeth have this much in common: Keeping your mouth shut hides them both. If you have a good opinion about a baseball topic, look for a better one.
  
  (6) Watch a some decent movies about baseball. Sugar is excellent and disturbing. Baseball: A Film by Ken Burns is available on Netflix and worth watching. You drink his nostalgic Flavor-Aid at your own peril: At times, Baseball is about as edifying as having a good, 19-hour stare at a Norman Rockwell painting. It's still in a class all its own as a baseball documentary. You should also watch Ed, starring Matt LeBlanc, because it'll teach you not to take strangers on the internet seriously when they give you advice.
  
  (7) When you go to games, wear whatever the hell you want. This has nothing to do with understanding baseball, but it annoys me when people make a big deal out of policing the clothing that others wear to sporting events. Sitting front-row at a Yankees-Tigers game in your best Steelers jersey and a pink Houston Astros BP cap? Whatever. You be you. You be you. I once watched as a perfectly innocent college student was denied a free t-shirt from a Nats Park employee because he (the student) was wearing a Red Sox shirt with his Washington cap. That was pretty fucked.
  
  (8) Take the EdX Sabermetrics course. Others have recommended this, with good reason. It's a wonderful introduction to advanced analytics, and you get a taste of programming in R and MySQL as well. You don't need a CompSci background. I sure didn't.
  
  Hope this helped.
  
  Footnote: Chad-hating is actually too easy. Truth is, I've never really been mocked for scoring games. Once, I even bonded with a Chad-esque guy sitting next to me at a Braves-Nats game here in Washington. He was pretty drunk, but we talked Braves baseball while he drank and I drank and I scored the game and he drank more. He seemed utterly engaged by the scoring process in that guileless, doe-eyed way that only the drunk have mastered. That's the Chad I loved.

You say you don't want to be a bandwagon fan. Who cares what people think? If the Cubs excite you because of their young stars, then go for it. You're only a bandwagoner if you stop caring about the team when they do poorly.

As far as home runs, the Washington Nationals have Bryce Harper and Ryan Zimmerman, who are absolutely on fire right now. The Yankees have Aaron Judge, hopefully Gary Sanchez when he comes back, and Greg Bird if he starts hitting well. Obviously I'm biased though. I don't know how much time you have on your hands, but if you want to learn about baseball history, Ken Burns' "Baseball" documentary is absolutely INCREDIBLE.

As far as rules, just ask around if you see something, people here are pretty good about helping newcomers.

Watch Ken Burns' Baseball documentary collection. This is the best way to learn about the origins of the game, its most famous players, most important moments, records, championships and traditions. It covers pretty much everything from the American Civil War thru present day. Can't recommend it enough.