It depends on the material, and the finish.
Very often, light color shoes in leather have a finish on them that won't let dye penetrate, so you won't get black with dye. There's leather spray, but in my experience, that cracks.
Vinyl or other man made shoes cannot be died. They can be sprayed with a colorant for man made materials, but again, cracking when going from light to dark, and also, depending on the material, a sticky feeling when dry.
Fabric shoes can be died, but not always to black. Black dye will often take on the undertone of whatever the original fabric is, so you may end up with a dark brown. Dyed shoes also have a tendency to bleed color into the shoe, onto your foot.