to increase you power rating (PR) to battle you need to build more ships. The more ships you build the higher your power rating.
Be careful however as ships also have an upkeep that is to be paid every turn out of your income to keep the ships. This can send you into debt very fast (especially with scouts) and sometimes force you to restart the empire and start over.
Each ship has a set of shields (energy, absorption (kinetic), ECM (missile) and chemical (biological)). Some of the shields are positive, others negative and some neutral at 0. Negative shields means that the ship takes XX% more damage from that sort of damage. Positive shields reduce the damage by the XX%.
Have a read of the manual regarding the ships weaknesses and other aspects (click on the question make (?) near each thing if your unsure what they are on about and a handy info screen pops up and lets you know what this and that does.
If you have any further problems or questions, don`t hesitate to ask as the community is very friendly as are the staff member.
Hope you enjoy yourself and anything your unsure of just do a quick scan of the manual first, you may find it, you may not but then again you may find something you didn`t even know about like a new trick or something! Very handy.
Enjoy and hope I helped clear this up.