Early in the game, you will end up in a 'compromising position' (you'll know it when it happens). To escape, you must construct a homing beacon, using the datacorder item you obtained before this point. The information needed to repregram the datacorder originally appeared in the Space Quest 6 manual as a brain-teaser puzzle; you can find that info here. If you can't solve the puzzle (I feel your pain), look here to see the specific configuration of circuts needed to engage the beacon.
Note: even after the beacon is complete, you must be standing outside for it to actually work.
Later in the game, you must "borrow" a shuttlecraft. In order to power the ship, you must enter the proper intermix elements in the appropriate control panel (use the buttons on the dashboard to navigate the ship's menu system). This puzzle requires you to apply information from the game manual to information within the in-game intermix menu itself. Click here for the information from the manual needed to solve this puzzle.
Clear as mud, right?
If you still can't figure out what to do (it IS a rather obscure puzzle), click here to see the specific settings to enter into the panel.