Are there any vedic texts that describe/teach the art of dancing? If not is there a vedic text that describe the dance of lord Nataraj?
Well, we have the various Upavedas associated with the four Vedas. Dhanurveda, Ayurveda, Gandharvaveda etc.
There are four Upavedas: Dhanurveda, Gandharvaveda, Ayurveda and Arthasastra. Some schools hold Sthapatyaveda as the fourth Upaveda instead of Arthasastra.
Dhanurveda is the science of warfare. Gandharvaveda is the study if aesthetics and it speaks of all art-forms like music, dance, poetry, sculpture, and erotica. Ayurveda is the science of health and life. Arthasastra deals with public administration, governance, economy and polity. Sthapatyaveda relates with engineering and Architecture.
All these sciences/arts are discussed not just from their technical perspective (though that is primarily done), but also as a means to transcendence.
Therefore, Gandharvaveda is the scripture you are looking for.
Each of these Upavedas are related to one Veda or the other. Gandharvaveda is related to the Samaveda.
Gandharva veda, the upaveda of the "Sama Veda," is the study of all art forms including music, dance and poetry. This Vedic text contains information about the laws and ways to practice music as well as how music works as a therapy to heal the body and soul. Gandharva veda uses the music of nature to restore balance of body and mind.
Gandharva veda also offers a detailed account on the the association of music with various aspects of creation and the positive impact of music on the body and mind. It also gives insight on the association of different sounds and rhythms with different species on Earth.
Gandharva veda is effectively used in meditation as it helps the yogi transcend to the innermost level of the mind.
This page lists some instances where the term Gandharvaveda is found in various Hindu scriptures.
The Shiva Purana (by J. L. Shastri)
Chapter 1 - Origin of the sacred lore < [Section 7.1 - Vāyavīya-saṃhitā (1)]
There are eighteen secular Vidyās—Āyurveda Dhanurveda, Gāndharvaveda etc. ending with Arthaśāstra. 27
The Mahabharata - Third Book (by Krishna-Dwaipayana Vyasa)
Section XCI < [Tirtha-yatra Parva]
And having thus acquired weapons and mastered the Gandharva Veda, thy third brother Vibhatsu liveth happily
The Brahmanda Purana (by G.V. Tagare)
Chapter 35 - The legend of Yājñavalkya’s receiving the Veda from the Sun-God < [Section 2 - Anuṣaṅga-pāda]
The Āyurveda (Science of medicine) The Yajurveda The Dhanurveda (Military Science) The Sāmaveda The Gāndharvaveda
Vedicreserve gives the names of the two texts that are dedicated on this particular Upaveda.
- Natya Shastra (PDF)
- Sangita Ratnakara (PDF)
Natya Shastra (translated into English) can be bought from here too.