If you're traveling on a weekday, you can take the Purple Line Express to/from the Sheridan station (about two or three blocks north of Wrigley Field). The Purple Line Express only runs rush hours only, so it would be post-game for a midday game, or pre-game for a night game.
At all other times, you'd have to take the Red Line (which boards on State Street, about 3/4 of a mile east of Union Station) to the Addison Station, which is one block east of Wrigley Field.
If you take the Brown Line, you'd have to get off at either Belmont (a half mile south of Wrigley Field) or ride over to the Irving Park station, which is 3/4 of a mile west and a few blocks north of the stadium (this would be pretty far out of your way).
If you're traveling during rush hours, again, I'd recommend boarding the Purple Line at Washington/Wells or Quincy/Wells, which are the first two stops on that route in the loop. The rail system gets extremely crowded during rush hours, especially with the construction going on, and Cubs traffic can, at times, overwhelm the system.
To go back south to the loop after the game, I'd suggest walking north on Sheffield to the Sheridan station, because if you try to get on at Addison, you might have to wait for three or four (or five) trains to go by before you can fit.