A typical job-shop machine shop has an hourly rate anywhere from $50 to $200 an hour, depending on capability, backlog, and so forth.
Most will charge one hour minimum, even if the job takes 20 minutes, and more than a few will charge two as soon as you're more than a few minutes over that first hour.
Then again, some shops are fairly friendly and will be glad to help you out- if you're not in too much of a hurry, they may put it in with some other low-priority jobs for when the employees have a few minutes between jobs, or finished one job but it's too late in the day to start the next big one.
And yes, you need to have your ducks in a row when you take it in- full dimensions are a minimum requirement, drawings would be ideal. For a single simple job, an actual printout paper would be superior to trying to give them a CAD or other digital model. Do NOT just say "take off about this much" or anything like that. Unless you're leaving part of the design work up to us- and are willing to pay for it - we want hard numbers and acceptable tolerances.