I know that the person who does your nails is a "manicurista" but I don't know the conjugation for getting a manicure. For example, if I was offering to pay for my wife's manicure, I would say, "would you like to get a manicure" or "would you like to get your nails done". But I don't know the same conjugation to ask that question in Spanish.
In short, you would use hacerse [las uñas/la manicura] as an auxiliary verb, pretty much in the same way you use the verb to get.
To complement Gorpik's and Ustanak's answers, I'd like to add a couple of ideas:
Spanish is slower than English to make verbs from nouns, (especially neologisms), and the reason seems to be the need for verb endings that imply the creation of additional neologisms rather than giving new meanings to the exisiting ones: it just does not sound right —at least at first—. While in English there is the verb to manicure, in Spanish the best (and only?) choice is to add an auxiliary verb to the noun.
Unsurprisingly —for foreign words—, both the noun and its gender change depending on the region, hence you have:
- Hacerse la manicura in Spain. (Thanks CarlosAlejo)
- Hacerse la manicure in Chile. Pronounced [ma.ni'cjur]: the closest one can get to the French pronunciation with Spanish phonetics, I think.
- Hacerse el manicure in Colombia. (Thanks Nicholas J.)
We have no specific verb for that in Spanish; we'd rather use hacer la manicura. Both your English options have an easy translation:
Would you like to get a manicure? --> ¿Quieres que te hagan la manicura?
Would you like to get your nails done? --> ¿Quieres que te hagan las uñas?
Notice that in Spanish we tend to use the passive form less than in English. These are good examples where we would use an active impersonal construction rather than the English passive.