OK ive been looking into this recently and what you need is an Aramex "Shop and ship" account. Go down to an Aramex shop, (one near decoration roundabout) or one of their booths (think they have one in landmark?) and set up an account with them. Think it costs around 120 riyals to open an account with them, but they said after the end of this month it goes up to 160 riyals i think (take an ID copy with you).

Once that's done, you will have a mailbox in both the US and the UK (and I think one in China aswell). You go on amazon/ebay or whatever, order your stuff to one of the Aramex addresses, and they ship it over. You then get a text message when the item arrives, you go down there, and depending on how much the item weighs thats how much you will pay for the shipping.

Im having a guess, but I think they said it costs around 45 riyals for the first kilo, and then around 35 for every additional kilo after that. But the minimum you can pay is the 45ish riyals for the 1st kilo.

Other than that there is no additional cost, enjoy :D