The first thing to ask is if describing the accent is necessary.

It might be my love of period pieces, but my dialogue tends to have a British accent in my head, but I'm not going to write that into my story. It's not necessary. Not to the story, not to the character.

However, some characters have an accent that differs from the majority of the other characters. An example that jumps out at the moment (since I'm reading it to my daughters recently) is Hagrid in the Harry Potter series. His dialogue is written to be a bit rougher and a little less "civilized" sounding. This is important to the character, since it's very much a part of his characterization. That being said, J.K. Rowling never specified a British accent to her main characters.

Hagrid's dialogue is punctuated a lot to show where he leaves of letters and combines words, or even words spelled differently to allow for the altered pronunciation. For a classic example: "Yer a wizard ... an' a' thumpin' good'un, I'd say".