Comedy stands alongside adventure, drama and horror as one of the things Doctor Who contains in many stories and gives pride of place to in a few. This is something that often happens around the gaming table anyway, but more out-of-character than in, and comedy in gaming can feel forced. (I’ve played some great games of Toon, but also some really flat ones.)
One good method is to play up the absurdity of a situation while attempting to keep a straight face, like the piling on of country house murder mystery clichés in The Unicorn And The Wasp. The players should start reacting to it in character, and that sets the ball rolling so they start ticking off ideas and suggesting more.
The easiest method is to have a go at Doctor Who itself, but this is too easy. Better to have comedy monsters which are rubbish in-character like the Slitheen rather than rubbish out-of-character like Cybermen with lace-up boots.
Other methods include absurdity cranked up to surrealism played lightly, satire and parody.
The ultimate aim is to make the players laugh. Whether the characters do or not is unimportant, but in this case it’s possible for the characters to have fun as well.
Example: The Gap
(A Comedy Aliens Of London story)
“Doctor, are you really telling me that aliens have taken over a motorway service area?”
“Well, you wouldn’t think to look here, would you?”
“But... this may be the obvious question, but why?”
“Oh, I dunno, dispersing themselves around the country without anybody noticing, sneaking onto lorries, and... ooh, a soft play area!”