How do you upgrade ship in dark orbit

You don't upgrade, but purchase a new one.
There are several different ship types you can purchase and get rid of your craft. Nowadays you pilot two crafts as a noob, the Phoenix (the tiny, really really wimpy one) and the Liberator (better but still pretty bad. :P)
here are the ships and their prices. If the ship is uri the credits bid will also be displayed:
Phoenix: Free but only if current ship is destroyed
Yamato: 16,000 credits
Defcom: 32,000 credits
Liberator: 64,000 credits
Piranha: 80,000 credits (Buy this one. I designed it XD)
Nostromo: 100, 000 credits (Fastest non-uridium ship in the game)
Bigboy: 200,000 credits (Slowest ship in the game, strongest non-uri ship)
Leonov:10,000 uridium I suggest 500,000 to 1,000,000 credits bid. (noob ship)
Vengeance: 30,000 uridium Bids are often 20,000,000 to 40,000,000 credits
Goliath: 80,000 uridium Bids are anywhere from 50 million to 200 million credits.