Blessings for the Sick and the Afflicted

If you or someone you know is sick, injured, or otherwise unwell, you can get a blessing for that person. If you don't know any Mormons who can help you get one, you can contact the local missionaries or a local Mormon leader by using these tools on Mormon.org:
http://mormon.org/missionaries   http://mormon.org/meetinghouse

If using the meetinghouse locator, you can find the bishop's phone number if you click on a meetinghouse, click on a congregation that meets there, and click on the Leadership tab beside the Schedule tab.

If you just want the blessing and are worried about someone starting a discussion on beliefs, make your intentions clear. Mormons (missionaries especially) are happy to help random people just because. It's one of the main purposes of the church we belong to.

Members would not expect or wish to be paid for giving a blessing. Mormons consider it their responsibility to give freely of their time to help others, so to suggest to pay them for their service would probably make them uncomfortable. But you could probably get away with buying them a hamburger or something as a way of saying thank you if you felt it necessary.