to research anything, you need a research center.
it can be destroyed by enemy attacks ( it's not easy to destroy, 3500 hit points are needed).
you don't need any manpower but a lot of time to build a new one.
There are four kinds of inventions that can be researched:
basic researches ( needed for following inventions)
ships ( without ships, no movement in space ;) )
to produce ships you need a shipyard.
like the research center it can also be destroyed by attacking fleets (also 3500 hit points).
you can only produce ships that you have previously invented in a research process.
all the ships in your base can be recycled. you get the manpower free to produce new ships.
(you will not loose points this way)