Would a Young Single guy in his 20's with US degree have any luck getting a Job?
Who should he contact?
Like Gina said it is easy and US degree is appreciated. You can look at the sites Gina posted those are good ones.
As for whether first you should move to Dubai and then go job hunting i dont think that is such a good idea as living in Dubai without a job might burn holes in your pockets. First submit your CVs or even if you have someone living in Dubai tell them to submit your CV for you. Give the numbers of the place you are living presently in and also emails. Let them contact you.