Starships go directly to the reserves.
Look into "Shipyards" and there click on the Tab on the right, If I remember correctly it is named "Fleets".
There you should find your Ship
To deploy a Taskforce right-click on a System which has a Mobilization-Center (at the Beginning of the game usually only your Home System has one of those and choose "Deploy Taskforce". Here you can build Fleets of certain Sizes with the Ships in your Reserve and they appear one turn later in the System where your deployed the Taskforce