Show them. :) It's always best to lead by example. Have your Non-player characters use specific references and attitudes that can be easily copied -- however clumsily at first! -- and keep on hammering them with good examples until they get the hang of it.
If and when players lapse into American-speak or other characteristics you don't want to encourage, again rely on your NPCs. Have them misunderstand, react poorly to innocent comments, and provide other negative reinforcement (tho as little as necessary) to illustrate the worst-case scenario.
As noted in other responses here, reward it when they try. Keep the rewards small at first, but specify clearly exactly how much they're getting for which comments, attitudes, and actions. Then increase the rewards in response to more and better attempts. Next thing you know you'll have started a trend... and the better players of such roles will be getting bigger and better rewards. They'll keep leading by example, taking a lot of the load off your shoulders.
Finally, find written works (if you can) that can supply both ideas and one-liners that can be used or copied by the players. Such things will vary widely by setting and culture, else I'd recommend specific examples.
Best of luck!
Geniuses are Hard
It's easy to play a person stronger or faster than you, since we have an objective sense of how to scale up stats. A really agile character is just that- like you, just more agile. But mental stats are a lot trickier. We know what it's like to encounter a smarter/wiser/more charismatic person, but that doesn't tell you how to think or act like one. This is especially a problem when it comes to social characters, because lots of games like to have your social checks modified by how well you can roleplay. This can penalize the player for wanting to be that particular type of character. So how do we make it easier for socially awkward people to have highly charismatic characters?
We cheat.
A common way to play more intelligent characters is to have the GM feed you extra info. You can directly ask the GM for hints on a puzzle, tell you if plans might have problems, etc. We can do a similar thing with manipulative characters: the GM and other players can work with out-of-game to make their characters easier to manipulate.
Everyone's Just a Giant Pile o' Buttons
In order to influence someone, you need to know about them. Everyone has likes, dislikes, hopes, fears, secrets, etc. Your character could have some mechanical way of finding these out, where your GM would work with you to make that way effective. The better you do, the more you learn and the more audacious you can be. A minor success might be listening to gossip or doing some internet stalking. A major one could be looking your target's ex to spill everything to you during a drunken sadfest or even getting a look at his diary.
Note this opens up a lot of interesting roleplaying opportunities as a side effect of learning the information, as opposed to a requirement for learning it. The difference is that your success is guaranteed, so the roleplay is about determining how you did it instead of about determining if you can do it. This is a great place to work with the GM and other players: if Dave is so paranoid about people seeing his diary that he keeps it in his backpack at all times, what circumstances gave you a chance to peek?
I Feel You Bro
A good manipulator can sense how other people feel, almost like a sixth sense. In this case, that sixth sense is metagaming. If players tell you what their characters are feeling and why they're feeling that way, your character can know it.
Let's Not Mention That I Killed Your Dog
In order to persuade someone you have to know how what you say will impact them. Normally this is pretty hard, because most people don't even know themselves about how they'll respond to things. Fortunately, the players and GM have complete control over the other characters, so you should be able to ask "How will telling you XYZ affect your character?" and get a mostly accurate response. This helps you map out what your character should or shouldn't say and then pick the 'right' choice to get what you want. In game, of course, it will look like your character intuitively knows just the right thing to say. You can flip this around, too: "How can I get you to react this way", which helps if you can't think of what to say but your character can.
This also leads to some great opportunities to play out manipulation gone horribly wrong. Under some cases people should be able to lie to you and make you do the wrong thing. Alternatively, they could say "Your character thinks ABC will happen, but actually DEF will".
Summary
It's easier to play a charismatic character if everybody else at the table is helping you make the character charismatic. This means giving you extra info or working with you in the roleplaying parts so that your character can better control their characters. It's your character that's supposed to be cunning, not you. You shouldn't be required to do the heavy lifting.
Best Answer
The successful dumb characters I've seen aren't just dumb. Develop the character as much as you would a character that's not supposed to be dumb.
I find that characters who use one syllable words or weirdly bad grammar but seem otherwise unimpaired get boring pretty fast. Your character can often follow his friend's lead most of the time, but when he is left on his own, he makes mistakes, or does the obvious in combat. If his friends told him to do something and the situation changed, have him continue to do what they told him to do because he doesn't understand why he's doing it in the first place.
Also, don't overdo it. You probably rely on others for figuring certain things out, but you can remember how people have treated you. If people are condescending to you, you can tell unless they are subtle about it. When it becomes obvious you've done something stupid, you get ashamed, or angry, or are embarrassed and don't want anyone to mention it. You don't use complex sentence structure, but you usually speak normally enough that it isn't immediately obvious that you are dumb.
This can be fun for the table because it's kind of a problem solving exercise to give your character instructions that cover enough possibilities but aren't too complicated to understand. Some problem solving and strategy things are kind of out for you, but you can spend that time figuring out what your character's understanding of the situation is. To a point - you might want to ask everyone's help in not having the plot be a series of riddles or puzzles, unless they specifically give you something to do (e.g. your character is in a riddling contest matched up against a talking chicken "What am I sitting on?" "An egg". "What do I like for breakfast?" "An egg." "Where do chickens come from?" "An egg". "What came first before a chicken?"...).
For a really dumb character role playing them realistically would probably not be fun, since they mostly have no idea what is going on - it would be like trying to role play a dog. If it's a comic campaign where you are as dumb as would be funniest at that moment it might work OK, but it probably gets old within a few sessions at most. Or not. If you are having fun don't let me stop you - I'm just thinking about other people's characters that have worked out for my taste.