The ship designer can be accessed by clicking the "Designer" button at the top of the screen while viewing the map or by the "Designer" button at the bottom of the Ship List in the Shipyard screen.
Once in the designer, you can either create a new design or modify an existing one. The buttons to do so are located below the ship list on the left hand side of the screen. To modify an existing design, select a ship from the list and click "Modify". If "New Design" is selected, the ship list will be replaced by the Hull template list, which will allow the player to select a starting block to build off, or an existing template design.
Galactic Civilizations III is integrated with the Steam Workshop and allows the sharing of ship templates. The "Steam Workshop" button at the bottom of the screen will open the workshop and allow players to download hull templates (these ships are not equipped and will appear in the hull templates panel not in the build list). Custom designs can also be uploaded when saving them.