The central portion of the bridge contains a door on the left hand side after you first walk through the doorway into the bridge. It is through this door that Toshiro Kago will enter if he's still alive. The captain's chair is toward the front of this area. There are controls to fire the death ray and (to the left of that button) three other buttons to adjust the ship's shields. A death ray aiming workstation is to the left of the captain's chair (although the player cannot operate it, Sally manages to do so). Along the sides of the room are four generator-reset buttons, two on either side of the main bridge compartment. A holographic image appears above a button if that button needs to be re-set. A forward observation area is located below and forward of the main bridge area (reached by stairs on either side).
When looking out the window on the bridge you will notice 3 buttons to the left of the main button that fires the Death Ray in the quest This Galaxy Ain't Big Enough.... The further to the left you go, the higher the shield power goes up, but this also lowers the power of the death ray, and vice versa. The best strategy to destroy the enemy alien ship is to alternate between pushing the button on the right (providing maximum power to the Death Ray) to shoot, and pushing the button on the left (powering up the shield to max) when being fired upon by the enemy ship. That should make short work of the enemy ship, and thus end the final quest of the expansion.
The death ray can still be fired and the shields adjusted after the completion of the add-on storyline.
Items on the bridge (including alien corpses and companions) will never disappear, so if the player chooses they can use it as player housing. On the console version of the game, the only way to remove the alien corpses is to completely disintegrate them with a weapon, including the torso. The game will eventually automatically clear the pieces left over.
There are several interesting objects outside the playable area of the Bridge (which can be found by using the tcl command on the PC version) including: Two intercoms, an odd rectangular prism with the texture of the bridge's floor on the top of it and alien computer and light textures on the sides, and non-functioning "secondary" teleporters under each of the visible ones.
The stasis chamber located in the room with a teleporter to the Capital Wasteland can be opened and this allows you to put items inside for display. Once they are placed inside the chamber, it can be closed and you could see any items placed through the glass.