The 60 minute addition is the bittering addition and should be in the longest. Add shortly after the break (froth and potential of boiling over) has past. These hops should be in the boil for at least 60 minutes. Boiling shorter will lessen the bittering of the beer and upset the balance. Leaving them in for longer is OK as most of the bittering compounds are extracted by 60 minutes.
15 minute hops should be added with 15 minutes to go. 5 minute addition should be added with 5 minutes to go. You should not boil the wort after these times are up; these are flavor and aroma additions, and the delicate oils will evaporate if boiled for longer.
When you reach the 0 minute time, the heat should be shut-off, the pot removed from the heat source, and the lid placed on. Once boiling stops, you will not lose any of the delicate hop oils, so it is not critical (from a hop extraction point of view) to cool immediatly. Some people like to steep the wort after the boil (between 15 and 30 minutes), before cooling as they believe it extracts more aroma from the hops.