Bootblacking is in general care for somebody's boots, usually a leather of some sort, given the prevalence of Leather Fashion in the scene.
One should usually start with removing shoe laces, if any. Asking if the tongue of the shoe should be cleaned is a good idea when applicable, as that part of the shoe generally doesn't see so much dirt in comparison, and thus doesn't need to be cleaned as often. Then putting a thin layer of water on the boots to help spread the soap more easily. When soaping, you don't want to let the soap sit very long, as it may get absorbed into the wet leather otherwise. The soap is spread with a brush and wiped with a rag, generally cotton or some specialized fabric.
Next comes polishing. Note, before starting you should make sure you have the appropriate shade for the boots to help bring out their true color, as opposed to conflicting. This is generally done by hand, wearing surgical gloves or something water-tight, to help prevent the bootblack's hands from being stained. After applied, a brush is used to remove of excess. Only use it on the material, as the sole usually requires separate things for it.
If the polish isn't toxic, and presuming permission has been given, the bootblack will be able to lick the boots, now that they're clean. This helps show how confident the bootblack is in their work.
Ends with replacing the lace for anything that needs it.
It is also a very different thing doing it while someone is wearing the item and after it is removed, though either are options, depending on the situation.