The Bug Off is a competition between you and your Animal Crossing: Wild World neighbors to catch the biggest bug. After catching a bug, you turn it in to Tortimer, who stands outside of the Town Hall throughout the competition. He will tell you if your bug is the biggest so far. A neighbor might turn in a bigger bug after you turn in yours, though.
There are four Bug Off competitions per year. They take place during the summertime, on the third Sunday of June, July, August, and September. The contest begins at Noon on those days, and ends at 6PM.
Winning the Bug Off is as simple as having a bigger bug to give to Tortimer than any of your other villagers. The best way to win is to turn in a bug that is one of the biggest types available in the game (see the list below).
Tortimer will stand outside of the Town Hall during the contest. If you have a bug in your pockets, you can talk to Tortimer, say you caught a bug, then choose the bug that you want to give to him. Tortimer will keep the bug, so be sure not to give Tortimer a bug that you were hoping to keep! Tortimer will tell you how big your bug was, and will tell you if yours is the biggest one so far, or if a neighbor has turned in a larger bug.
Be sure to talk to Tortimer again from time to time before 6PM, because he will tell you if a neighbor has turned in a bigger bug than you have. Sometimes it is in your best interest to give Tortimer your bug shortly before 6PM, to reduce the chance of a neighbor handing in a bigger bug.
Each type of bug in the game has an average size, but its real size is a random number somewhere close to that average. The only way to find out a bug's size is to give it to Tortimer during the Bug Off. The following bugs are the biggest in the game:
Note that some of these bugs cannot be caught during the contest time. In particular, the biggest bug in the game, the Oak Silk Moth, cannot be caught during the contest. You can catch an Oak Silk Moth ahead of time and keep it in your house until the time of the contest. Tortimer will accept it.