Some shelters euthanize using the "shot" method like a veterinarian.
Many shelters, particularly in rural areas, use other methods of euthanasia. This can include:
Gas chambers/rooms where a bunch of animals are put in all at once and gassed (yes, very Hitler-like)
Heartstick where an electric device similar to a cattle prod is used to shock them into death
Shooting. Pretty self explanatory. Basically, it's cheaper to buy bullets than the chemicals used in humane euthanasia.
Some shelters don't even euthanize animals, they just sell them to labs for experiments. Then they go to the city council and brag about how the shelter makes money for the city.
It's sad but that's the way it is. Animals are treated like property and disposed of in the cheapest, easiest manner possible.
Until people start spaying and neutering their pets and taking responsibility for said pets, these things will continue.