This is a pretty thorough guide.
http://www.gamesradar.com/f/the-2008-pc-builders-bible/a-20080918153014865039
Building your own computer:
Pros:
-You decide what goes into the computer (don't pay for what you don't need)
-Often cheaper (the price difference gets bigger as the price goes up)
i.e. a $400 Dell and a $400 custom won't be much different in performance but a $1000 Dell and a $1000 custom will show a clear difference in performance with the custom being much faster
-Parts are of higher quality (assuming you buy from reputable brands)
-Easy to upgrade (Pre-made computer cases are often not ATX standard and their PSUs are usually not powerful enough to handle many upgrades)
Cons:
-Each part has its own warranty
-If the computer breaks its up to you to figure out which part broke (this is quite easy though)
-Due to the ATX standard, custom PC cases are often larger then pre-made PC cases
Buying a prebuilt computer:
Pros:
-Warranty covers the entire computer
-Don't have to worry about individual parts
Cons:
-Possibly pay for things you don't need
-Often comes with pre-installed software that is useless and slows the computer down
-Hit-and-miss customer service