You want the pop filter normally to be closer to the microphone than the mouth, maybe just about 1" away. Alternatively, you can use the pop filter as a way to keep a singer from getting too close to the mic by positioning it farther away.
You should be at least an inch or so from the pop filter, to reduce the amount of saliva that builds up on it at least. Mic technique for recording is typically very different from live mic technique. Usually I like to have the mic at least 6" - 8" from the singer's mouth when recording, which is way too far away for high volume live situations (it would work for bluegrass with no drums, though).
Mic position regardless of the pop filter isn't just a whole question, it's potentially a whole forum.
For most mics:
The closer you are, the more low end emphasis you get - even to the point of boosting the low end, which isn't always good. The more on-axis you are, the more even the response and the better the high end. The more pointed towards your nose or chest, the more of each of those parts of the sound you will get. Beyond about 12" - 16", the sound can thin out a lot, making the voice sound distant (which can be good for backing vocals), but also you get more of the sound of the room. More or less room can be good or bad depending on how good the room sounds and what kind of sound you're going for. Most rooms that are not build and treated for recording don't sound very good, although you can get special effects with some interesting rooms. Many artists have used bathrooms, stairwells, or long hallways to get different sounds.
Let's look at a few pros:
I notice they both use C12s or clones. Taylor sure has her pop filter close to that very expensive mic.
And Beyonce getting really up close: