Make sure this doesn't void your warranty: acquire cheap OGG-capable players that come without one.
Step 1: Tools You Need
3. (optional) Solder-stick paste, or rosin.
4. (optional) Solder wire or other soldering material.
Step 2: Disassemble the Player
This one comes apart fairly easy, you just pull the facing part up. Some are tougher: for example, the ones with a retractable USB plug often have to be pulled sideways first.
So, after taking out the screws, inspect carefully. The things that get stuck most often are the USB plug, the buttons, the battery holder, and screws you've missed.
Depending on the construction of the player, you may only need to take one half off to reveal the audio socket, like in this case.
Step 3: Inspect the PCB
1. the solder between it and the printed circuit board breaks; and
2. the narrow strips of metal that hold the plug in the socket become loose.
Try moving the socket element. If it's shaky, re-solder the pads (see next step).
If not, put the plug inside the socket full way. See if the metal strips on the socket touch the plug rings. If not, take the plug out, then push the strips on the socket inward using your screwdriver.
Step 4: Re-solder All Solder Pads Under the Socket
If it doesn't melt, your iron is too cool. (Get a cheaper-looking iron.)
If it doesn't stick or stays on the soldering tip, you might need to clean the tip in rosin again and retry; apply additional solder to the pad; or apply solder-stick paste to the solder pad (use the screwdriver).
When done with one pad, continue with the other two.
Shielded sockets have additional pads that connect the metal socket frame to the ground on the PCB. This one's plastic, though, so there's no additional hassle.
If your player uses an AA/AAA battery, you'll probably have to re-assemble it before testing.