Many amusement park devotees and season pass holders say that Tuesday is Great America's slowest day of the week. We tried going on a Tuesday, and found almost no lines, in spite of excellent weather.
Print out the list of rides at least one day before going to the park. Have everyone in your group choose the rides that are most important to them, and write up a list in descending order by priority.
Arrive at the park by 9 am. The parking lot will already be open. At around 9:30 the main turnstiles will open and you will be allowed into the front of the park to wait by a large carousel with a reflecting pool in front of it. You will wait there until 10 am. Being at the front of the crowd is crucial to getting to the most popular rides before the lines begin to build. A show starts soon after this to keep the little ones occupied. This is also an excellent time to take care of locker rental and visits to the bathroom, if you have someone to hold your place in the crowd. If you are going to split up as a group, now is the time to decide when and where you will meet again. Don't use precious ride time for negotiating these details!
Orient yourself on the map and plan your route to the first ride. As soon as security allows the crowd to pass through to the rides, make a bee line for your first ride. We did this and were able to ride the top four most popular rides before noon.
After you've ridden your highest priority rides, head to the back of the park. Most people ride the rides from the front of the park toward the back. Be aware that some areas, such as County Fair, don't open until 11 am. If you are there at 11 am when it opens, there probably won't be much of a crowd anyway, because most people are still working their way somewhat systematically from the front the park toward the back.