Over the years, I've spent many, many afternoons at Wrigley Field. This is one of the highlights of any Chicago trip; obviously, the baseball schedule will determine whether or not you have an opportunity to attend a game.
Most games start at 1.20pm. Some start later. The best way to kick off a day in Wrigleyville is to arrive early and preparty in the neighborhood. The stadium is practically surrounded by bars and restaurants. The Cubbybear is probably the most famous, but it's also the most touristy. On game day, a can of Miller Lite will be four or five bucks. Go a block away to Texas Star Fajita Bar for some decent Tex-Mex. On Sheffield (beyond the right field wall) there are two bars: Murphy's and the Sports Corner. Both are good places to primer.
If you have the prized bleacher seats, you might want to enter the gates early (at least 1 hour before game time) if you actually want a decent seat. On hot days in the summer, the most comfortable "seat" is to simply stand against the chain-link fence in right or left field, behind the seating area. You're simply a few feet farther away from the field, and you get a decent breeze.
Stick around through at least the seventh inning - sometimes someone halfway famous will sing. I've seen Jimmy Buffett do the seventh-inning stretch in the past. If anyone halfway cool is in town for a concert, there's a decent chance they'll sing at Wrigley. Always fun to see who it will be (just hope it's not Da Coach).
After the game, postparty in the neighborhood or walk a couple blocks away for any one of the good restaurants in the area. Sheffield's in a fun place...a few blocks south on Sheffield.
Note about tickets: Bleacher tickets can be hard to get, especially if a division rival is in town or if there's a good pitching matchup (i.e., Kerry Wood vs. Anybody). In fact, bleacher seats to almost all of the premium games sell out before the season even starts. If you are serious about attending a Cubs game, try to line up your tickets ahead of time, either by buying them the day the go on sale (in Feb. 2002), picking one of the rare games with tickets will available (Marlins, etc.), or get seats to the game you want via an online broker (at a premium, of course). If you really want to experience Wrigley, I would definitely advise getting into the bleachers, but I would not advise relying on the (semi-illegal) scalping scene on game day to get your tickets. It can be done, but if you show up on a Friday and it happens to be Wood vs. the Unit, you will be watching the game from Murphy's. The bleachers may not be suitable for young children, as it can be quite a debaucherous and well-hydrated crowd.