Unless other arrangements have been agreed upon by both parties, the user with less feedback sends/pays first. The exception is when both parties have greater than 10 feedback, and both users should send simultaneously at that point. Upon receipt, the opposite party must remit payment/shipment of their end of the deal.
Hint: if a user is strongly opposed to sending first, it's a telltale sign of a potential scam. Please use judgement when buying, selling or trading or ask another member that is trustworthy for assistance.