Production and Research
Research
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 ;) ) Buildings, and probes.
Production
To produce ships you need a shipyard. like the research center it can also be destroyed by attacking fleets (also 3500 hit points). You obviously can only produce ships that you have previously invented in a research process.
see also http://www.spacetrace.org/man/production_and_research.php
Recycle ships
All the ships in your base can be recycled. you get the manpower free to produce new ships. (You won't loose points this way)