There are times that phonetics can work. St-st-stutters, for example, are easy enough to render and can be read quickly; a character attempting to read a complicated bit of vertig- verbla- verbiga- verbiage can make for a good quick explanation of their lack of reading fluency. These, though, are tricks and should not be heavily used; to quote from "The Legend of Rah and the Muggles:" "Well, wha— wha— what do you know a— a— about dat! It's the ba— bah— bahbies Naddie and Neddie were tal— talking ah— ahbout," he stuttered to himself. One quick bit of stuttering, one word missed, one lithped eth, can give the effect you need without becoming overpowering. That said, if a character's speech impediment or accent makes them difficult to understand within the context of the book- that is, the other characters have difficulty making them out- don't be afraid to disguise the meaning for the reader. The Redwall series' moles did this well, and Terry Pratchett uses it too, for the Igors. The former have an incomprehensibly thick cockney accent; the latter pronounce all "s" sounds with a "th." All of them. Other characters sometimes call them out when they don't.
Personally, I would use phrasing to show that English is not the character's first language. For instance, an Irish person who is speaking English tends to overuse "after". So she might say "I'm just after coming from the shops and guess who I met?" A French person tends to occasionally drop the last letter of a word, or to over-pronounce it. Keep it subtle. The reader will remember that this person is not a native English speaker, you don't need to hit her over the head. Just keep sentence structure simple, and don't use words that you are not likely to learn quickly when you start.
In every single one of my books, none of the characters have English as their first language. But I don't use phonetic dialogue. That's largely because it's almost impossible to apply Gaelic pronounciation to English words, but also because it has no real purpose. The occasional use of a phrase in that language, often an insult or swear word that the character doesn't want everyone else to understand, also reminds the reader that they have an accent, or that they don't speak English as a first language. Not even patriots constantly talk in their own language, unless they are part of some sort of enclave that also speaks it. It's unrealistic, unnecessary, and annoying to have them persistently use their own words.
i'm reading a novel by anne perry right now, that's set in 19th century london and i find the maid's cockney accent, while done quite believably, is annoying as bleep, to read, since there's so much of it... so, as for phonetics, a little does go a long way... and too much of anything good can be a bad thing...
