Purchasing the PSU depends on what make your computer is, if it is a Dell or a couple of the other OEM machines you will have to purchase the PSU from them as theirs are made to their specifications are not ATX compatible.
If your machine is ATX compatible I would just stick with a known brand name like Antec, Thermaltake, etc. If you aren't sure how much wattage you will need try using the power calculator here.
Installing the PSU isn't complicated, it will only go in one way, and the connectors will also only go together one way. If you think you're going to get confused just count the number of connections you have and make sure that you have the same when you finish.
The one thing that you do need to do first is unplug the PSU from the wall outlet, and turn of the off power switch on the PSU. The rest you should be able to figure out once you see what's in there.
Three last things, be careful not to dislodge anything while your playing around in there, you might even go so far as to make sure that all the boards and RAM modules are all seated properly before you close the case back up.
While you have the case open do a little house cleaning, blow it out with some canned air...do not use your shop compressor!
Lastly, and most importantly...do not play with the old PSU, there are capacitors inside that will retain a charge for a very long time and have enough power to hurt you.