How do you pay another player diamonds? (For ex. paying them 50 diamonds for a item)

If you're the one paying, they actually do most of the work. What generally happens is that they set up an exchange in the currency exchange, in this case it would be 1gold for 50 diamonds. Then you go and buy that exchange (make sure it's the right one) and once they get the payment, they'll send you the item and it'll appear in your trades.