Some ships are pre-designed. Initially you will want to build
some factories and pump out colony ships. Usually at the easier levels
you don't have to worry about war ships later (on random maps). Eventually
you will want to design your own ships for speed and toughness.
One simple tactic is to colonize more planets than the AI. Don't worry
about who supposedly is first in the beginning. When you meet the AI, on
the stats page keep your eye on production. If you vastly outproduce the
AI, you are on your way to winning.
One of the main problems initially is money. After you produce some colony
ships, send out a few extra survey ships to look for anomalies that bring
in money. Eventually money problems disappear when you start producing
banks and stock exchanges. Researching democracy will help a bit. Also
researching good and evil and choosing neutral will get you a lot more free
squares to build on.