Look at your picture and think of a popular culture reference. You can either go for the blatantly obvious, or somewhere off in left field--either will work swimmingly.
Determine who in the picture can be associated with which character: Peter, the rotund and fumbling average guy; Lois, the obliviously seductive stay-at-home mom who married down; Meg, the homely and insecure teenage girl inside us all; Chris, the clueless son; Stewie, the intelligence and villainous infant who speaks with a British accent, engages in diabolical plans, and whose orientation is up for grabs. Brian, the dog, is also an excellent choice, being an insightful character who struggles with alcoholism and writer's block. You can also draw characters from any celebrity or famous person, living or dead.
Once you've determined your characters and your pop culture references, you need to really let loose with silliness and humor. SInce the "Family Guy" thrives on silliness and non-sequiturs, it is relatively easy to come up with a joke that could be used on the show.
Share your picture with your friends. Send them an email with your attempt at cleverness on display. You could end up brightening someone's day.