Narada as we know him now was actually a normal boy of a maidservant in his previous birth. Due to association with some asectics he devloped faith in God and practiced meditation and austerity. Pleased by his devotion, Vishnu appeared before him for one time and said that only in his next birth he will be able to associate with God. So Narada led that life as an ascetic (muni) singing the flories of Lord. When after pralaya (annihilation of the whole universe), when creation began next time, Narada in his present form came into existence along with the other rishis:
After 4,300,000,000 solar years, when Brahmā awoke to create again by the will of the Lord, all the ṛṣis like Marīci, Aṅgirā, Atri and so on were created from the transcendental body of the Lord, and I also appeared along with them. [SB - 1.6.30]
So Narada is known as a muni. And regarding his Veena, it was given to Him by God:
And thus I travel, constantly singing the transcendental message of the glories of the Lord, vibrating this instrument called a vīṇā, which is charged with transcendental sound and which was given to me by Lord Kṛṣṇa. [SB - 1.6.32]
The Linga Puran chapter 2.3 has also description regarding how Narada as an ascetic performed penance and obtained his musical skills. I'll add it when I have made the translations.
Shrimad Bhagavatam 1.5 and 1.6