Here you go ryan. This is in chronological order.
Spring Training:
This goes from beginning of February to the end of March. This is basically just practice for 2 months to get back in shape. The game during this time have no meaning on the actual regular season.
Regular Season:
There are 2 Leagues: the American League and the National League
There are 3 Division in each League: East, Central, and West
This means that there are 6 total divisions.
Major League Baseball Teams play 162 games a season usually starting in the first week of April and last through the last week of September, maybe even into the first week of October...81 games are played in a teams own stadium and 81 games are "on the road" which just means at other teams stadiums.
There is no real structure to the regular season schedule except that the teams compete in mostly 3 and 4 game series with an occasional 2 game series mixed in. When I say series I mean that the same 2 teams play games against each other in that series at one stadium. For example a 3 game series that has the Phillies play at the Braves means the two team will play 3 games over 3 days in the Braves stadium. When looking at a season schedule the "away" team is listed first and the "home" team is listed second. So using the example above you would see Phillies @ Braves on a schedule. Also most games are played within your own League....meaning that National League teams play mostly National League teams and American Leagues play mostly American League teams, but there are some "Inter-League" games mixed into the schedule which means that certain National and American League teams will play each other.
During the regular season teams compile Wins and Losses for the games they play. At the end of the season the the teams with the most wins in each of the 6 Divisions I mentioned above are declared "Division Champs" and are moved on to the "Post Season" or "Playoffs". Those 2 words mean exactly the same thing.
There are also 2 "Wildcard" teams, one from the National and one from the American League. These 2 teams are basically the next best team behind the Division Winners and usually have the 4 most wins in their league. Each Wildcard team also qualifies for the Playoffs making 4 team from each league able to play in the Playoffs or a total of 8 teams.
Playoffs/Postseason:
This is the part of the season that every team wants to make it for, but only 8 qualify. In each league there are 2 playoff series going on to start. I believe in the first round this is a 5 game series, which means that in order to advance to the next round a team must win 3 out of the 5 games. This is called the Divisional Round.
After the Divisional Round your have the American Leagues Championship Series and the National League Championship Series...commonly referred to as the ALCS and the NLCS. This puts the top 2 team from the American League against each other and the top 2 teams from the National League against each other in a 7 game series. This means that the winning team must win 4 games to advance to the next round.
After the ALCS and NLCS you have the grand daddy series of them all called the "World Series."
This is also a 7 game series that puts the winner of the ALCS against the winner of the NLCS meaning again that the World Series Champion (the best team in baseball) must win 4 games. Last years World Series (2009) had the Yankees from the American League against the Phillies from the National League play, with the Yankees winning the 7 games series, 4-2 making them "World Champs"
I know it's a lot to read, but I love teaching about baseball and I could go on forever. Hopefully it's more helpful than confusing. thanks