"Hello. My name is Doctor X. I'm a new doctor in the area and was wondering if you need a psychiatrist. If so I can fax, e-mail, or mail my CV."
From this alone you'll likely get people literally jumping to get you to work there. Now this might not be every single area of the country but it would be the overwhelming majority.
They'll likely ask for job references as would anyone in any place of employment.
As for a CV, you don't have to ask us. If you're a resident ask the faculty in your program. In this stage of the game you should already have good CV experience.
During fellowship, my PD looked at my CV and gave me several ways to correct it, but that's different. If you're a forensic psychiatrist, you could have a cross-examining laywer try to destroy you on the stand simply based on your CV even though there's nothing wrong with it. E.g. they might try to make you lose credibility simply because the font didn't look good. I'm not joking. During a mock trial, the cross-examining lawyer told me my CV should be thrown out because the pages weren't numbered. Of course it wasn't, but that's how BS these things can get.
I'm digressing but I had one case where a lawyer tried to have me taken off as an expert witness when he asked me how many competency evaluations I did, thinking it woudl've been on the order of just a handful. I sat there, told the judge I would need to calculate it becuase I lost track, and I said something to the effect of...
I don't remember just how many, but based on the fact that I've done at least 2 a week for one year and did about 15 before that, I'd say at least 120.
But if you're very worried about this, several famous doctors including my fellowship PD have their CVs online. Just get their CV and use it as a template for your own.