I am writing a story that features an illiterate Indian woman. Of course, while there are things only Hindi can satisfactorily express, I was wondering what would be a good way to construct dialogues for someone like that- an illiterate woman in her forties, world weary.
(Just finished reading the Mayor of Casterbridge. Not sure if I could pick up much from there though.)
What's more important? Her inability to speak in English? or her story that will be narrated? And even if you began writing disjointed sentences as an attempt to show that she is not a native English speaker, are you absolutely sure that the readers will keep on reading it? Disjointed, grammatically wrong sentences are fine in dialogues. But only when you use them sparingly. They are used as a tag to say 'this guy is not a native English speaker' or 'this girl comes from a not so elite social environment of the English classes'... or you get the drill. Perfect example, the character of Eliza in G.B Shaw's Pygmalion who had a cocknea accent with a not so good grammar. And this is London we're talking about.
G.B Shaw was so (obsessed is the right word?) with phonetics that there are some instances where he wrote Eliza's dialogues in cocknea English accent and then provided the proper worded dialogues in brackets for those who couldn't get it the first time. Pygmnalion was a play. Yours isn't. And this is not Edwardian London. My point is, what matters is your story and your characters. When the characters are developed fine, they seem real, they'll start speaking.
Again, don't worry about the way your dialogues will appear. Worry about the story. Those hints will be enough in the beginning because when the reader will be half-way through the story, they won't be concerned with the way she speaks. They will be concerned of what's supposed to happen next.
Your best bet is research. Find a "Little India" community, wander around, and listen. Sit at a corner coffeeshop for a few days. Walk through the retail area. Don't stalk people, but pay attention to who is speaking and what they're saying.
You may get just a lot of Hindi, but if you're in an English-speaking city, you're bound to find someone speaking in broken English.
Lauren's answer is the best way I can think of to go about it, but if for whatever reason you can't or don't want to do as she suggested:
A person who isn't a fully competent speaker of any language, like English, will normally carry over idiosyncrasies from "their" language. The main example I can give is that home-language speakers of Afrikaans, which uses only one word ("is", pronounced like the "iss" in "hiss") for both "is" and "are", very often use "is" and "are" inappropriately; some, because of the similarity between the English "is" and the Afrikaans "is", barely use "are" at all.
Another common slip-up I see with Afrikaans speakers is grammar, specifically word order. People tend to instinctively use the sentence structure used in their mother tongue, rather than that in the new language.
Unfortunately, I don't know anything whatsoever about Hindi, but I get the impression from what you wrote that you do know the language, at least to some degree. Look at the sentence structure and anything peculiar to the language, and use those as starting points. Although I wouldn't recommend using them as-is in dialogue, word-for-word direct translations of Hindi sentences would be a good way to find these idiosyncrasies.
One last note about word choice: The difference between a technically correct word and a situationally correct word is one of the last things someone learning a language grasps. Using not-quite-right words can be a good way to convey that someone doesn't speak a language well, while still making what they're saying fully comprehensible to your reader.
The first example that comes to mind is that while "He was driving very quick" conveys the same idea as "He was driving very fast," only one seems correct to an English speaker; not so to someone new to the language, who only knows the broad meaning of the words.
