If you have a shipyard and a ship is stationed at it, then when you select the shipyard there should be an area on the right hand side of the selection details box in the lower left hand corner of the main screen which shows icons for each ship stationed at the shipyard. Click on the icon of the ship you want and you should see a dialogue menu pop up which says 'eject' and a couple other things, off to the right of the selection details panel. Click 'eject' and your ship should pop out of the shipyard. Alternatively, you should be able to click on the ship icon and then click somewhere on the main map to get the same effect.
If you don't see a ship icon in the selection details panel of the shipyard but you do see an empty box on the right hand side, hover your cursor over the area and see if you can find the ship. The box fills with ship icons starting in the top left and proceeding to the bottom right in the same manner as English text is normally written.