An Imperialism shipyard is one of the pre-built buildings in your capital. It is used for building merchant ships (over which you have no control) and warships (which you can then see on the map and direct).
As with the other unit-building facilities, the shipyard offers a menu of (up to eight) possible ships you can build. Click on one and you see its statistics, a description, the cost per unit, and how many of each required item you have. Click the right-facing arrow button to increase your order. If you want to order one but have insufficient items, you may leave the window open while visiting other buildings to reduce their requirements so that you have enough for the ship.