How do I speed up egg hatching?

As Toomai states, having a Pokémon with Flame Body or Magma Armor helps tremendously.

While the effect of having two Pokémon with the same ability doesn't stack, the efficiency of the ability can be multiplied by up to five by carrying more than one egg at a time.

Finally, there is a bit of a trick that'll significantly simplify the issue: When on the Bike Road, half of your movement is handled for you, and an unblocked avenue that runs from top to bottom can be found on the far left side of the bridge.

This means that you only have to press and hold the up button on the D-pad; and this can be done with a rhythm that is very easy to do with complete absence of mind, often allowing you to at the very least read or watch something else as you slog along.

If you have a Pokémon with Flame Body or Magma Armor in your party, then each step towards hatching eggs will count as 2 steps (halving the number of steps needed). The effect doesn't stack if you have multiple Pokémon with the ability at once.

For future reference and people who find this through the search dialog, I'll add some sneaky tricks for other games:

Diamond / Pearl

These 2 games contain the Tweaking glitch, which lets you enter the "Void", which is the black area outside of the visible map (parts of that area can be seen when you're standing close to a wall in a building). In this area, since there are few colliders, you can walk/run/bike indefinitely (actually, around 65000 steps before you run into something, but yeah...) as long as you find a clear path (which exist in great numbers). Numerous resources on the Internet explain how Tweaking works and what paths exist (although most are related to reaching Darkrai or Shaymin).
Note that this bears the risk of your game freezing when you Egg hatches in an area that would make it freeze if you saved, so it might not always work and you might need to find different paths for each number of steps.

To run indefinitely without actually pressing the D-Pad all the time, just put something heavy (like a can or some heavy tool) on it that locks it in position. Some sort of clip or tape might also work.

If you're using a 3DS, you can use a small coin to lock the joystick in any direction. This also applies to the Gen 6 trick.

X / Y

In Lumiose City, the Plaza outside the Prism Tower is round and contains a clear path all around. Just go there and lock the joystick as described above. Talonflame is a great Pokemon for hatching as it has Flame Body and can learn Fly (to get to the Central Plaza faster).
Also, don't forget to use the Hatching O-Power to speed the process up even more.

General

This is just pointing out the obvious (and is implicit to Willihams answer), but you should always ride your bike while hatching. This increases the rate of steps vs. actual time spent.