In more detail:
Each question is given a weight proportional to the disparity between the yes and no responses. A question that is answered yes and no by an equal number of people has no weight, since your answer to a question that 50% of people answered each way does not tell anything about your weirdness. A question that is answered entirely one way or the other has maximum weight. If you answer the same way that the majority do, the weight is subtracted from your score; if you answer the way the minority did, the weight is added to your score. The result is scaled to give a value in the range of 0% to 100%, such that if you answer the way the minority did to every question your score is 100% and if you answer the way the majority did to every question your score is 0%.
Here is an example for a hypothetical four-question test. The fraction of previous test-takers who answered the questions yes are 80%, 40%, 50%, and 75%. The weights of these questions are the differences between those values and 50%: 0.3, 0.1, 0, and 0.25, giving a total weight of 0.65. Your answers to the questions are yes, yes, no, and no. The weirdness you accumulate for each question is -0.3, 0.1, 0, and 0.25, totalling 0.05. Scaling this gives you a Weirdness Factor of (0.05 + 0.65) / 1.3, or 54%.
Note: Until November 2005, the Weirdness Factor was calculated in a different manner.