In the "vanilla" or default game as far as I know you can not build anything.
There is a mod on http://xelerus.de/index.php?s=mods
Actually there are a slew of decent and great mods on that site. I STRONGLY suggest that you select your name on the game (where your name comes up) enter a new name and hit enter then start a new game and try out various mods. You need to restart the game once you get the array of mods you like.http://xelerus.de/index.php?s=mod&id=413
allows player stations later in the game.
More stations are found here: http://xelerus.de/index.php?s=mods&c=Station
BTW there are longer versions of the game here: http://xelerus.de/index.php?s=mods&c=Adventure%20Extensions
Which when all are installed allows you to choose one, thus you do not need to install/uninstall mods in order to play.
If you install a player ship mod (perhaps others as well) you may note that special items from that ship will show up in game. For instance I installed Enterprise E
--> Player Ships: http://xelerus.de/index.php?s=mods&c=Ship%20%28Player%29
--> Enterprise E: http://xelerus.de/index.php?s=mod&id=258
Which has "Star Trek" weapons. Those weapons are showing up in my other games even though I am playing with the Millennium Falcon.
--> Millennium Falcon: http://xelerus.de/index.php?s=mod&id=294
I know that the Search Tool here is frakked (Frelled) so you have to use the official forum site for searches. http://www.neurohack.com/transcendence/forums/
Use the search tool most of your questions have been asked before or there are 'hints' you can uncover.