It works pretty much like any other online shop, find the thing you want, choose how many and then click the buy button. Create an account if you haven't already and then choose your payment method, I use a Visa debit card and get charged a pound or 2 for the currency conversion.
Aliexpress hold on to your money until you confirm you've received the item and its working, then they pay the seller.

As with ebay don't pay a seller privately, use the system on the site.
An exception of this would be if you really know you can trust the seller, like I've bought stuff directly from chai as he has a reputation of being an honest chap. I don't think anyone from aliexpress has built such a reputation with the CNC community yet though.