Get there early!! Earlier than that even.....I'm talking seriously early!!
June 2002 my DD (then 7) and I were at MK at 7:55 for a PS at the Crystal Palace (our PS was for 8:10). We ate a great breakfast, got some super pictures in front of the castle with no one around, saw the Mouse himself (got pics and autographs) and positioned ourselves directly behind the velvet rope into Fantasyland. Once the rope dropped, we were on the first ride of Dumbo, rode the Carousel, Peter Pan's Flight X 2, Winnie the Pooh, and Snow White's Scary Adventure. We got Ariel's autograph and then headed into Toontown Fair where we rode the Barnstormer three times, toured Mickey and Minnie's houses, got Cinderella's autograph (as well as running into a LOAD of character by the train station). By the time we boarded the train, it was MAYBE 11 o'clock and we had not stood in a single line. Before the rain set in at around 2 o'clock, we had done BTMRR, Country Bears, visited Tom Sawyer's Island, went on the Haunted Mansion and had lunch.
The next day we went to the MK at opening again and it was once again empty ( we left at 10 o'clock for a PS at the Grand Floridian).
It was unbelievable and amazing. I just didn't understand where all the crowds were. SOOO, my best advice is get there early.
I'm sure lots of others have more advice....