I can talk in general terms about ship design, colonization, and the like, but this is an area where the resources we've already recommended have a lot of info.
To begin with, you need a survey ship of some kind. This is usually a fairly simple ship, just a few engines, a couple survey sensors, and some fuel. The most confusing part is probably the design of the engine, but you need to do that from the "Create project," screen before you can design any ship that you expect to move. I've already mentioned how you design engines, sensors, and weapon systems in earlier messages, but it's basically just picking elements from several lists, and then researching or instantly giving yourself the technology.
Another thought I had, would it be easier if you maybe started a new game and told the machine to design your first ships for you? That might let you explore the rest of the UI with ships which will generally work, though you lose out on the mechanical experience of designing things from scratch.
The basic flow for the ship design window is this.
1. Hit the "New class," button.
2. Hit "rename class," if you don't like the default name the game gave for the class.
3. Move to the component tree view and look around, find engines, and expand the category to find the engine you've already designed.
4. Route your mouse to the engine you designed and double click. This is a bit tricky with your resolution, but should work if you use the mod.
5. Go to the ship design display, which will show you the ship is now able to move faster than 1 KM/S.
6. Repeat for survey sensors or other components you want to add.
7. Close the window.
8. Retool a shipyard (on the shipyard tab) for the design, which is again just a matter of selecting a yard with the proper tonnage and type, selecting "Retool," from the list, and pressing the "Set activity," button.
This same process, with variations, is followed for all ships you want to design, or for bases, fighter craft, etc.