How to network to people while working as a nursing contractor?

I was hired by an agency to be a lead RN in a seasonal flu shot clinic in a medical center. Most of the hospital employees will be getting it and I want to ask any tips on how to network, hand out resumes so I can be hired directly.

How to ask if a position is open without being awkward? If you wanna give your resume really bad what should I say? How will you start a good conversation?

Hoping you could help me guys! Thanks!
This could be considered a conflict of interest. So I am not sure I would attempt to hand out resumes. Could also be a HIPAA violation, as the only way you would know any of their names are by the fact you are providing a medical service.

Likely a violation of your contract with the agency. And everything above it would not be just awkward it would be unprofessional to bring your resume to a contract job to solicit employment.

Handing out resume's would be inappropriate.You could start a casual conversation with statement's like " I really like this facility, how long have you been here, tell me about your unit"... etc.Keep your ears open .. Good luck!