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Look for freight-forwarders locally. They will combine your stuff (boxed and labeled) in a container with any other house moves heading in the same direction. Depending on the popularity of the destination it can take a few weeks for a container to fill. It then takes 10-14 days to ship to the USA and a few days to reach the city at the other side (depending how far inland you are)
If you deliver boxes to their local depot in your city and collect from the port/depot at the other end it will only cost a few $/kg by sea. They will also collect from your place and deliver to your destination address for more $$$.
They handle all the paperwork, customs etc.