The Rajya Sabha (meaning the "Council of States") is the upper house of the Parliament of India. Tamil Nadu elects 18 seats and they are indirectly elected by the state legislators of Tamil Nadu. The number of seats, allocated to the party, are determined by the amount of seats, a party possesses during nomination and the party nominates a member to be voted on. Elections in within the state legislatures are held using Single transferable vote with proportional representation.
Source: Parliament of India
Source: Indian government (Rajya Sabha) website
Rajya Sabha election in Tamil Nadu, 2013