If you have a problem with an order, the first step should always be to contact the seller. To contact the seller, either click on the order number on the [orders placed] page and click Contact your seller about this order, or go to Problem > Order, type in the order number and choose Send Message. If the problem is missing pieces, try to be as clear as possible as to which pieces are missing; if an order hasn’t arrived, ask the seller when the order was dispatched and when they expect it to arrive.
If you haven’t received a response from the seller, go the the problem order page, input the order number, and choose File a Non-Shipping Seller Alert (this can only be done after 7 days since the order was placed). This will alert BrickLink that the seller has not shipped the order and may cause the seller to respond to you. If you paid with PayPal (which is highly recommended), log into PayPal and file a dispute. PayPal is bias towards buyers, so it’s very likely that you will get a refund fairly quickly.
If you paid by some other payment method like cash or cheque, you may not be able to easily get a refund (and laws are different in each country as to what the process would be here). If you used another online payment service, search their site to see if they have a process similar to PayPal for disputing a payment and getting a refund.