This is challenging because some lasers go slow (blasters) and others go fast (Life destroying moon that was badly named, even star energy sucking base was bigger)
I challenge that the Death Star beam goes slow. You have plenty of time to see the thing form and travel. It ostensibly goes much, much slower than the speed of light. I don't think it's mentioned to be a laser either. Ultimately it doesn't matter, the Death Star is a plot device, you can't deflect plot devices anyways.
Let's say you're not set on lightsabers and blaster bolts being made of lasers, because the movies never mentions them being lasers. If you delve deep into the Expanded Universe, you'll find many rationalisations of what is most likely just 1970s Hollywood science (the Kessel run in 12 parsecs anyone?). But when taken at face value, what the movies show ain't lasers at all.
In some "science of videogames" thing on Star Wars and lightsabers, Michio Kaku explains how we could, with today's technology, build a lightsaber. Something about a ceramic blade engulfed in hot plasma. The caveat here is you'd need a small nuclear reactor to power it, and you have a solid ceramic blade that's isn't very sexy. Still, the idea of plasma is also common in the Star Wars EU to describe blaster shots. Therefore:
Everything is plasma
Plasma can be summarily described as an ionised state of matter. Plasma can generate a magnetic field.
If you consider a lightsaber is a plasma torch (with the blade shaped not by some physical ceramic tube but rather with the Force or some complicated space-age technology) and magnetised, and consider blaster bolts are magnetised bits of plasma, then it's magnets being repelled and that's just science.
It might also explain why lightsabers don't cut each other, because their magnetic fields don't allow them to pass through. And it also explains how some materials are impervious to lightsabers, since, as mentioned, some ceramics can sustain a whole lotta heat.
Okay but actually want to shoot real lasers too
What you're looking for here is refraction. Simply put, when light changes medium (going from air to water for instance), it turns slightly. You can observe this with a glass of water, and then moving your finger behind the glass. You'll see a lot of weird things happen to the image of your finger. That's light being refracted.
Now your lightsaber blade is a hot plasma. This is an inherently different medium from breathable air. A laser being made of light will be refracted, and appear to be deflected. Now I'm not sure you could deflect a laser back that way, but you can conceivably deflect them away from your person and that should be good enough.
As for being able to react in due time, as @Renan mentions Force-users seem to have the ability to feel the near future. It might be best illustrated in A New Hope when Luke deflects his first blasters from the training remote, explaining
I did feel something, I could almost see the remote.
It's not really clear how it works, but it evidently does work.
 In some languages, they're actually called lasersabers, but we can chalk it up to bad translation. Especially when the title translates to The Star War.