Again not as simple as you might have thought, in the past it was quite common to have a PSU come with the case you bought, these days it probably won’t but that’s not such a bad thing as the included ones weren’t that good. Again similar to the case, once you have got a decent PSU you won’t need to change it for a while if you’ve bought correctly. The first thing to do is to make sure its compatible with the motherboard, thankfully most of the better PSU’s connect to most motherboards. They do this by having twenty pin connections with a further four pin connector that fits alongside the twenty pin one to cater for either twenty or twenty four pin motherboard sockets and they usually have a further four pin connector for any extra graphics requirements that your motherboard may have.
I usually like to spend a bit more on a power supply and get one with a fairly large power output capability so it has plenty in reserve. Some of the cheaper PSU’s were rated at 350 Watts which doesn’t give you much in terms of today’s power requirements and I would consider 500 Watts to be a minimum and 750 Watts is not unusual.
Remember all the time your computer is on it will be making some sound so I always try and go for silent or low noise components because of my personal hatred of noisy computers. A nice “extra” feature that some of the better power supply units come with are detachable cables. If you’ve seen a power supply unit before it’s a small cube with a lot of cables sprouting from it, you won’t be using them all so by being able to unplug some means your wiring will be simpler and take up less space leading to a better air flow and cooling, which leads (if you’ll pardon the pun) me nicely onto cooling.