janhardo, you sound like a newbie. Are you? That would explain a lot. For the moment, I'll assume you are.
The key to getting new ship-types is Research. The first step is to research the parts that you want your future ship to have (i.e., drives, weapons, defenses, range, support modules, etc.)
Once your race understands the parts, there are two ways to get the ships you want; the simplest way is that they will just appear on your shipyard availability list immediately after you have researched all of the necessary parts.
The second way is to go into the Designer and design your own ship. The Designer is pretty easy to use, and can be very very effective, the more so as you gain experience and learn what you need & want.
Very useful for me is the following website that allows you to compare the various ship-parts so that you can design exactly the kind of ship you want.
http://galciv3.gamepedia.com/Ship_parts
Hope this helps. Post again if you have more questions. There are lots of people on this site who will be glad to help.