The way nails are usually cut when playing the finger picking style is as such:
Note: This is described as if the gutar player is right handed, thus his picking hand is the right hand.

The Thumb is usually the longest of all the nails, typically it is used to play the bass lines. The nail usually get to be quite thick as it takes the most abuse. If you are looking at the back of your hand the nail is cut at a greater than 135 degree angle, before 180 obviously. It is cut this way so when your hand rests where it is supposed to, while playing the guitar, that edge of your nail is what you use.
The rest of the fingers are the exact opposite. They are all cut somewhere between 45 degrees and 0 degrees.

The nails do not come to a point, rather they are rounded. It's hard to explain, just imagine that that all your nails peak to one side.

Cutting your fingers in such a way are merely preference. Almost always the left hand nails are cut short so you don't click on your fret board. Some people prefer to have no nails and just pluck harder to get a louder sound. As with most things involving guitar it has a lot to do with the guitarist opinion.

A good example of how the thumb needs to be loud is MalagueƱa, which is an old Spanish folk song.