I have pictures from the various steps above.

Start with the Pi and solder some 26 awg wire to it:

I used red for the left audio to pp26 near the audio jack (thank you pi foundation for labeling the solder pads)

solder black for ground to pp24

right audio is a yellow wire and you solder it to the upper left pin on the audio jack.

UPDATE: 3-26:

Some more testing showed to me that PP24 directly to the metal pad is ground PP25 is right audio and PP26 is left audio. Picture of updated solder pad usage attached.

I recommend leaving the wires long 3-4" you can trim them down or tuck them in later. I leave them long because my projects often get pulled apart and rebuilt/re-purposed. I really like this particular 1/8 in jack. I chose it because the clear top means you can see and understand exactly how it works.

Soldering The Audio Jack (The pinout is in pics above):

Take the red wire from the pi and solder it to pin 2 on the 1/8 in jack.

Take the yellow wire from the pi and solder it to pin 5 on the 1/8 in jack.

take the black wire and twist another 3-4" length of black wire to it then solder to pin 1 on the 1/8 in jack.

solder a 3-4" red wire to pin 3 on the 1/8 in jack.

You should now have an audio jack connected to the pi, if you were to play sound with headphones plugged in you would have music playing clearly on this jack. I reccomend hot gluing the wires on the bottom of the pi and the bottom of the jack in order to secure the thin wires and also to protect them from damage and shorts.