@Noel *********
you'll want to set an appointment with the DLT first or you'll end up being in Chiang Mai for a while. But at immigration in Chiang Mai you just need a TM30 and 500 baht for "express service" and you can pick up your residence certificate the next day. You should be able to find some information by googling it.
But if you roll up to the DLT without an appointment they'll check all your documents and then hand them back to you with an appointment like 2-3 weeks away.