First thing you need to consider, is that although a single LED has a very low voltage, very few (I doubt any, but I haven't checked them all) only actually have 1 LED. Normally it's an array of chips (depending on the number, it might be a mixture of series & parallel connections), which would increase the required voltage.
In order to drive at the correct DC voltage, a voltage converter is used. There's a few options to provide this (I'm going to very simply touch on each point, for more in depth details, you're best doing a bit of googling on the main points):
- Transformer to reduce the AC voltage, then rectify to DC - transformers are big, heavy & expensive. They use the magnetic field generated by an incoming AC current to generate a current in an output. By using a different number of coils of wire on the input & output of the transformer allows the voltage to be increased or decreased. - This option is very rarely used in modern LED lights.
- Rectify to DC, then use a Linear voltage regulator to reduce the voltage - The least efficient, so not used for large loads or large voltage changes. Essentially, this drops the voltage by causing a volt drop over the regulator (these get hot, as they're very inefficient & "waste" is dissipated as heat). If this was used, using a 100V supply, a 1V load would be 1% efficient, a 50V load would be 50% etc (assuming all elements to be 100% efficient).
- Rectify to DC, then use a switched voltage regulator - These are generally quite efficient. They switch the incoming supply voltage to give an "average" voltage of what's required, which is smoothed to provide a constant voltage at the level required.
I'm not sure of the actual % of how efficient an LED light is, but from memory, they're in the "several 10s" of % efficient (which is a huge bonus over the <10% of incandescent & <20% of CFLs).