The survey ship you start with is made with a medium hull. You don't start with the tech for it, so you can't build it. You will have to research Zero Gravity Construction to get medium hulls. There are several techs before it. You should go to the tech tree as PUREVENOM mentioned in Reply #5, then look in the Engineering section to see what needs to be researched.
You don't need to do this to get a survey ship. At the beginning of the game you can build a ship called Guide that is a survey ship. You will need an Administrator to build it. It is weak and unarmed, so don't use it for anything dangerous.
As the Admiral said, you can design your own ships at any time, but you will be limited by the techs you have researched. The survey ships the game designs after Zero Gravity Construction is researched aren't very good, so I have designed my own. I could have designed some before I could use medium hulls, but I waited so I could put enough weapons and defenses on them.
I forgot to mention earlier that nearly everything has a tool tip associated with it. That is very important. You can learn a lot by putting your cursor on something (anything) and reading the tool tip. They are basically a manual. You should do this while in the tech tree to learn where things are. You can put your cursor on the name of a tech and on the icons that are below the name of the tech to learn a lot about them. Again, this works nearly everywhere because nearly everything has a tool tip associated with it. Try putting your cursor on things to see what you get.
If you want a real manual to read, there is one available in the game directory. If you have installed steam and the game in the default locations, you can find it in this location: C:\Program Files (x86)\Steam\steamapps\common\Galactic Civilizations III.
It will get less complicated and less confusing as you play the game more, so don't give up.