Birth to a Turkmen parent creates nationality. Birth in Turkmenistan alone to foreign parents is not unrestricted jus soli; territorial rules cover foundlings and otherwise-stateless children.
A child of a Turkmen citizen parent is a citizen (jus sanguinis), regardless of birthplace.
Ordinary naturalization requires about seven years of permanent residence plus sufficient Turkmen-language fluency and a legitimate source of income; grant is discretionary and renunciation of prior nationality is effectively required.