You have to research larger fleet size and additional capital ship crews.

The capital ship crew research is actually pretty expensive (and that's not even counting the cost of the capital ship itself), so it gets prohibitive to build too many of these.  The fleet size researches are actually pretty inexpensive, but they come at a very permanent trade-off: part of your economy is diverted to sustaining your heightened fleet size.  This starts low (9% at the first level) but when you max it out, 75% of your income is being drained.

Ever wonder how many people bought the game, never visited these forums, had the same issue, and then threw their hands up in disgust?

Based on your history of wonderful posts I think you would be excellent at it Darvin.

Unfortunately, it's very difficult for them to balance these things for all players.  A guy like me with 15 years of strategy gaming experience will beat the "normal" difficulty AI to a pulp on the first try.  The easy AI earns 50% less money than the normal AI, yet it's still a great challenge to people without that wealth of experience.  It's very difficult for developers to actually strike the right balance.

I will say that the most common beginner mistake is not expanding your empire quickly.  Bigger empires earn more money, more money allows you to support a bigger fleet.  Needless to say, smaller empires earn less money and have a smaller fleet.

Actually I just got through a game easily once I knew how to expand my fleet and make a second capital ship  It is hard if your fleet is limited and only have one capital ship to go against two or three but pretty easy if you can match them.  As I said, it was a brain dead question; but really hard if you don't know.