During this phase you can create new ship designs.  Designing new ships requires prototyping and testing by your empire, so the cost of the design is half the cost of the ship itself (rounded up).  This is a one-time research fee that will be deducted from the RU stockpile at whichever world you specify.  New missile designs do not require the one-time design fee.  See the Ship Design page for more details.

Once you have paid the design fee, you can build new ships of that type starting on the same turn.  The new ship design can also be given to another empire on the same turn that it is created.  You cannot design a new ship class on a world during the same turn that you take control of it, nor can you design on a world that is interdicted.