They really never explained how the spider sense worked.

It's like a precognitive ability that allows him to see 3 or 4 seconds ahead and that's way he can dodge bullets at point blank shot.

When something bad's about to happen, everything/everyone around Spider-Man goes into a super slow-mo. To him, Spidey's moving the same rate as he would normally move, but in reality, he's moving extremely fast compared to everyone else. He might not know what's about to happen, but at the rate he's moving at, he should be able to dodge/counter whatever's endangering him.

When something bad's about to happen, everything/everyone around Spider-Man goes into a super slow-mo. To him, Spidey's moving the same rate as he would normally move, but in reality, he's moving extremely fast compared to everyone else. He might not know what's about to happen, but at the rate he's moving at, he should be able to dodge/counter whatever's endangering him.

@cattlebattle: To be honest, I have no idea. That's the way I thought it worked for any medium, lol.

From wikipedia:

Spider-Man's "spider-sense" manifests in a tingling feeling at the base of his skull, alerting him to personal danger in proportion to the severity of that danger (Crofts 2011) . It appears to be a simultaneous, seemingly clairvoyant response to a wide variety of phenomena. Though the exact mechanism of this ability is unknown, his original spider-sense clearly has at least two aspects in addition to sensing potential or immediate danger:

• A psychological awareness of his surroundings, similar to the radar-sense of Daredevil. When he is temporarily blinded, Spider-Man learns to emulate this ability and navigate without his eyesight. Even under normal conditions, his spider-sense helps him navigate darkened rooms, instinctively avoiding obstacles or hazards, or potentially noisy or unstable floorboards, walls or ceilings that may betray his presence. In one comic, he is shown sensing how many fingers Mary Jane is holding up.
• An ability to detect certain radio frequencies. Spider-Man's technical skill is such that he has designed spider-tracers that broadcast a signal detectable by his spider-sense.

So as you can see, it was never fully explained in the books. I think the way it worked in the Spider-Man movies is how it works in the books, but that's just me.