How do I tell how worn my disc brakes are and what are the consequences of letting them wear too low?
It depends if your brakes have some kind of adjustment for the brake pads' position or not. An adjustment for "the point in the lever’s throw where the brake actually engages" (from Avid's description of their Contact-Point Adjustment system) can have similar effect. If they don't, they're worn out when you have to smash your brake levers all the way down to have any kind of breaking (but you could figure that out).
If you can adjust the pads' position, which is good because you can use your pads longer, then what you have to check is that the area showed in the picture (I couldn't find a word to describe it)
isn't used all the way up to the metal plate (the copper part of the brake in the previous picture).
So how do you tell how worn they are? By comparing to their original thickness. The pads use up quite linearly (Observation, I have nothing to back this up)
The consequence of letting them wear too low is that if you brake without any "breaking surface" left on your pads, the metal bits could get stuck somewhere and ruin your disc.
You need to replace your pads when they are about 3mm thick including the backing plate. You should be able to see how thick they are with your wheels off but you might need to remove them from the callipers to be sure. See the manufacturers site for details of how to remove and fit the pad - its normally an easy job.s
If you do need to change the pads on hydraulic brakes you need to make sure the pistons are all the way back, otherwise there won't be enough of a gap between the pads and the disc. Its best to do this while the old pads are fitted by using a flat bladed screwdriver to push them apart.
The other thing to remember is that the new pads will need bedding in before you use them in anger.
If you do wear the pads all the way down they won't stop you very well and they will make a mess of your discs.