Where can I get my clothese dyed?

I have a light cream silk skirt and there's some discoloration on it when I wasn't careful ironing it. I want to dye the whole skirt to a black color so the discoloration won't be visible anymore. If it was dyed, would the color still be there? It doesn't seem like the garment was damaged or anything. Also, where can I get it dyed without doing it myself?