The word for 'nail', in Spanish, is 'uña' (fem.). The verb in English 'to get done' is a little hard, and depends on the context. In your sentence, Miki, this phrasal verb could be: 'arreglarse' (verbo reflexivo); I was searching this verb in other context and it is hard. But, the translation could be:
'Me arreglé las uñas en la estética' or 'Me arreglé las uñas en el salón de belleza'.
@_@ K. Z.