If you need to know what your actual damage output in any given mission is, accounting for range, crits, energy drain what abilities you had active and when etc. you'll need to get a combat parser as defcon posted above.

If you just want to change a weapon/console/power levels etc. and want to see what it changed: Go into a system map (ie. Earth Orbit, outside DS9 etc) before you make the change, run your mouse over your weapon on the HUD and note the DPS. Then swap the weapon, console or whatever and note the DPS. It'll also show you what your theoretical DPS on each weapon will be if you activate your buffs (I say theoretical, because it doesn't account for crits, enemy resistances, energy drain etc. So your actual DPS will be different). This doesn't work in sector space.