Senseo & Raspberry PI soldering circuit board
It sounds like you want your RPi to be able to press the 3 buttons on your Senseo device. From the other tutorial it sounds as though this device operates on 3.3V, 

I would use a multi-meter measuring for continuity with the device unplugged/off. Prob the two points I have arrows to, if your meter beeps than these would be shorted together indicating ground.


Then I would solder your ground lead to the ground leg on the button to the left. Use your continuity tester to determine ground legs on the other 2 buttons. You will want to solder the wire to the non-ground legs on the other buttons. So it may look like this...

Then close up your device with your wires ran outside. Strip the ends of these wires and ensure that they are not shorting. Use a multi-meter to measure voltage to each button in reference to your ground wire. Ensure that you are only seeing 3.3V as anything higher will fry your RPi. Let me know if this helps. The second image is my best guess as to how your wires would need to be but with out it in front of me it is just a guess!