How to reach out to a job recruiter?

I'm trying to find a job and a recruiter for the industry I'm interested in recently added me on LinkedIn. I would love to reach out to him and build a connection, see if there's any way he can help me find a position, but I just don't know where to start since I haven't really contacted recruiters directly in the job search process so far. Would it be weird to reach out to him out of the blue? If it's fine to do this, what kinds of things should I say (I imagine it's not as easy as "hi I would like a job please find me one")?

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