A friend was describing an excellent but eccentric plumber who was working on his house. At one point, halfway through the working day, the plumber set down his tools and said, "Shall us go for a walk round the village?"
Say it out loud. Shall us go for a walk?
Now try this. Shall we go for a walk?
Your voice will be different. You can't simply can't say Shall us go for a walk? without a hint of a West Country burr.
This is the best - the only way - to write dialect. Forget funny spellings, forget apostrophes, it's all in the rhythm of speech, phrasing, grammar - and use of dialect words, which I'll do tomorrow.