A PS3 yellow light of death is an indication of a major hardware malfunction. There are two main pieces within your play station that can have issues and cause the PS3 YLOD, the method you will need to use will depend on what exactly failed. The most common failures are in the power supply or the motherboard. As a rule, it is the solder joints on the motherboard that are the problem. Solder is the silver looking substance on electronic equipment that is used to keep tiny wires attached to circuit boards.
In two of the PS3 models, 20GB and 60GB respectively the problem seems to be overheating. While these are definitely not the only models with issues, they are the most commonly affected. Inside the unit, the many processes going on generate heat, and many times the internal fans just cannot keep the interior cool enough, which leads to pooling of the solder. Basically that just means it has returned to a liquid state and leaves wires and tiny circuits exposed to dust, debris and vulnerable to vibrations.
Soldering Gun
A PS3 yellow light of death fix can be as simple as using a heat gun to re-melt the solder and cover the exposed circuitry. You need to be very careful with this fix because if you use too much heat on the board you can scorch it rendering it useless.
If your issue is a power supply short or failure you will need to order a new power supply or get one used from a broken game system. In some cases a simple fuse or resistor replacement is all you need to be back in the game and that is a fix compared to the 0 or more Sony will charge you if you are out of guarantees.