Intellectual capacity is not contained exclusively in the INT score. What we think of as intelligence is contained to greater or lesser degrees in INT, DEX, WIS and CHA. The question you are really grappling with here is: How does my character think?
I try to answer this question by looking at which of these attributes is highest when I have created him. A character's highest mental attribute is going to be his main
way of knowing the world. If a character has a high CHA, whether his INT is high or low, his main way of knowing is going to be interpersonal; a character with a high WIS is going to have a way of knowing that is centred on intuition and observation; a character with a high DEX is going to know the world spatially and kinesthetically.
It will be easier for you to understand the ways in which your character is not smart once you have got a handle on the ways in which he is. That way, you can focus on redirecting your own intellect into the way of knowing the character is good at. People often have the idea that the way to play low-INT people is to have them make lots of perceptible mistakes; this is not actually a trait of low-INT people but of low-CHA people.
Instead, your character should try to direct attention away from himself in situations where he is not mentally capable and towards himself in situations where he is. Did you ever see
My So-Called Life? Jared Leto's character is the perfect example of what I'm talking about. (If not, rent it -- it's the
Firefly of high school soaps.)