Are you talking about a lack of intelligence, or a lack of eductation?
Just to be clear, as one is very different from the other.
Formerly @Crimson Archer, now @CA
The Militia - Protecting Paragon City through roleplaying since June 2006!
My character Holly isnt the brightest bulb in the box, expelled from school a few times and thought it was 'hip' to skip high school, her parents werent really there for her, so she grew up in her own world.
RPing her a little dull is pretty easy. During RP she'll ask more questions than usual is all, "Whats that mean?" "Whats that do." "Whats this?" etc. She knows alot about certain subjects but general knowledge isnt her strong point, shes not to the point of dumb in which she cant add 2+2 though, just a little dull.
Hell, back when i RP'ed Echo she wasnt in touch with the music/film/culture scene at all, people would make movie refrences and she wouldent have a clue what they were talking about. Roll with it and take it how it comes is the only way i could describe doing it. "Would my character know that?" type of thing. Ugh, hard to explain. 
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2.) Someone who who is utterly incapable of picking up on sarcasm
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which is incredibly easy to explain IC with partial brain damage to the frontal lobe.
I've got some experience playing "dumb" characters, myself (not that that says anything about me IRL... no really! It doesn't! Hoooneeeest!)
Most notably, I've got Iron Alligator, who has been utterly detatched from modern society since his teens. As such he is very much a child in an adult's body (well, more of a mutant super-strong lizard's body). He gets confused quite easilly and has some very childish tendencies such as disregard for consequences, charging headfirst into fights overconfidently and an unhealthy fascination with fire and explosions. He also doesn't know how to interpret certain social situations, bless the poor croc.
The fact I'm also playing Spiderslice in the same VG as Jane is in should be another definate sign that I RP some seriously dumb toons. xD
Anyway, the only way you can really RP as "dumb" is trying to figure out just how intelligent (or equally unintelligent) she is. If you don't want your character seeming immature or anything, then just have her clueless on certain subjects. RP her taking a while to get her head round certain jokes (and as mentioned above, sarcasm), concepts, or generally complicated stuff. That's the best way to describe it. To be frank, you can only really properly understand how to be dumb if you are dumb.
And that's why my description should probably be good enough. 
Yus, time for another inane thread.
I guess, really, I'm actually asking for tips on how to play characters that have lower intelligence than the player. Not a huge dip in my case, but still.
With my character Jane Lundgren I'm trying to shoot for someone who failed at their education, and was raised in a very stern "don't question things" manner. The problem so far though, is that my "incredibly loyal but rather slow" personality is veering towards two things:
1.) A child in an adult's body.
2.) Someone who who is utterly incapable of picking up on sarcasm ("you're being volunteered for a very special unit, Jane"), yet seems comfortable nattering away with an advanced vocab.
The second point is something I'll iron out by myself eventually (so far my characters have been fairly, if not extroadinarily, intelligent so flowery language has snagged onto me as a habit), but I'm trying to avoid the former. Jane is very much an adult, very much aware she's doing things children would never do, but...I still have a sinking feeling she'll end up that way.
Does anyone have any advice for this? I'm not looking to make a completely stupid woman, just one who takes things at face value. The closest to this I've done before is someone who'd yell at the top of his lungs before piling into his enemies. Adding depth to such a concept is tricky.