First of all, you're never going to "get" baseball by watching just one game. The thing about baseball is that its appeal derives in part from its long season and relative continuity from one year to the next. It's like watching a television series such as Babylon 5 where the story arc takes years to develop. As you become familiar with the team and its players, you become more aware of the season-long and seasons-long dramas that unfold.
Beyond that, true appreciation involves learning the nuances of the game. Knowing that certain situations result in the hitter attempting to achieve different outcomes while at the plate; knowing that certain situations mean that the defense will set up differently in anticipation of their desired outcome; knowing that while baseball is a team sport, almost everything that happens on the field often rely heavily on the actions of one individual.
In addition, thanks to the statistical methods developed over the years, baseball lends itself so well to debate. Because both individual and team performances are much more easily quantified and qualified than in the other professional team sports, debate over statistical relavance is paradoxically easier and more contentious. Nearly everyone can understand the basic statistical measures and what they mean. To this day I still don't understand how the NFL's QB rating system works, and I have a minor in mathematics.
But so far, I've only been talking on a high-level abstraction. What about watching an individual game?
It's very important to understand that baseball is a terrible television sport. Because of the way you have to follow the action on camera, you don't get a proper sense of things such as the vastness of the playing field and the positioning of the defense. In a seeming contradiction, because the action on most plays can be captured by a single camera, there's little need for replay -- which is why football works so well on television. There's so much happening on the field in a given play that you frequently need multiple cameras to see all the reasons as to why it unfolded the way the way it did. Those replays help to mask the fact that, like baseball, for most of the time in football there's actually very little going on.
The other appeal is what happens when the offense starts to pick up. There's nothing like baseball in the way that the offense doesn't change sides once they score. It doesn't matter how many runs you score, you get to keep hitting until you reach your third out. You get to continue to cheer (or dread if its the other team) the scoring until then. In addition, there's a built-in drama to having runners on base. Depending on the number, you can score as many as four runs on just one pitch. There's no equivalent to this in any other sport. In addition, there's no running out the clock, you still have to protect your lead until the last out is made. While incredibly rare, teams have overcome eight-run (or higher) deficits in the last inning to win the game.
There's no such thing as a tie. You play until there's a winner. Once again, the clock is a non-factor.
While you may see the relative inaction as a bore, that can be part of its charm. Nothing in sports is as dramatic or sudden as a home run -- especially those that literally end the game. Aside from the home run, that pause between pitches can help build the tension in a particular part of a game. For example, when an offensive rally is underway, a long at bat with plenty of fouled-off pitches causes the anticipation of what will happen to build.
I don't have a real strong closer to end with, but may I suggest you read Thomas Boswell's "99 Reasons Why Baseball Is Better Than Football." It was written nearly 20 years ago, and it's just as true now as it was then.