Saritha, if you want word-to-word meanings, I have edited my previous attempt:
pallavi
iDadu padam tUkki ADum naTarAjanaDi paNivaiyE nenjE
Oh mind/heart (nenjE), please serve (paNivaiyE) at the feet (aDi) of that naTarAja who dances (ADum) with his left (iDadu) foot (padam) raised (tUkki) [1].
anupallavi
paDa aravADa puliyadaLADa bhaktargaL jaya jaya enavE
puli patanjali iru kaN kuLira tillaiyilE
As he dances to the chanting of his praises (jaya jaya enavE) by his devotees (bhaktargaL) in cidambaram (tllaiyilE) to the delight of patanjali and vyAghrapAda (puli) [2] whose eyes (iru kaN - 2 eyes) were refreshed/pleased (kuLira) by the awesome sight, the snake (aravADa) around his neck (with its hood fanned out - paDa), and his tiger-skin (puli adaL) garments dance/move along (ADa).
caraNam
tiruvaDi shilambugaL galIr galIrena
tirumuDi iLamadiyoLi paLIr paLIrena
dhimi taka tarikiTa tOm ena tirumaal maddaLam adhira
shivakAmi maNALan tirucciTrambalam tanil punnakaiyODu
With steps so firm that the anklets (cilambugaL) adorning his divine (tiru) feet (aDi) make a ringing sound (galIr galIr ena); as slivers of light (oLi) flashing (paLIr paLIr ena) from the crescent (iLam) moon (madi) in his locks (tirumuDi) illuminate the skies; as the drum (maddaLam/mattaLam) that vishNu (tirumAl) plays reverberates (adhira) to (ena) the solkaTTu 'dhimi taka tarikiTa tOm', my Lord, the consort (maNALan) of SivakAmi dances in (tanilE) the sacred (tiru) city of cidambaram (ciTTrambalam) [3] with (ODu) a smile (punnagai) illuminating his features.
FOOTNOTES
[1] muttutANDavar in a beautiful composition asks the Lord why his left foot is the one that is raised in most places - some of the possible reasons he comes up with make him wonder, "is it because you do not want to bear your weight on that half of your body that has been given over to pArvatI?" OR "is it because your left foot hurts from having kicked yama to protect mArkaNDa?" - It is only in madurai that his right foot is raised - supposedly in response to the entreaties of a pANdya king who felt that his right foot must hurt after bearing his weight continually for all those years - so, to accede to his requests, Siva dances in the veLLi ambalam of madurai with his left foot planted and valadu/right padam raised. This incident is lyrically described by Smt. ANDAvan piccai in one of her compositions.
[2] The express purpose of the tANdava nrityam in cidambaram was to bless AdisESa and vyAghrapAda with an opportunity to witness the cosmic dance - AdisESa incarnates as the sage patanjali, and meets up with vyAghrapAda, and the Lord, without failing, dances for them in tillai, on the holy day of guru pUSam in the tamizh month of tai (January 15 to Feb 14), during the daytime, described vividly in naTanam ADinAr of Sri GKB.
[3] I think 'tiruciTTrambalam tanilE' can also be interpreted as 'in (tanilE) the hall/open space (ambalam) located in our consciousness (cit)'