How can I play dumb?

I have a half-ogre character at my local larp group, and one of the roleplay-enforced restrictions for half-ogres is that they have low intelligence. I often find myself biting my tongue not to say ‘smart’ witty things, or reason with others to work out the plot. Most of the time I just come across as quiet.

How can I play dumb and still enjoy myself?

How can I play dumb and enhance others’ enjoyment of the game?