Background: The Madurai Nayaks were rulers from around 1529 until 1736, of a region comprising most of modern-day Tamil Nadu, India, with Madurai as their capital. The Nayak reign was an era noted for its achievement in arts, cultural and administrative reforms, revitalization of temples previously ransacked by the Delhi Sultans, and inauguration of a unique architectural style. The dynasty consisted of 13 rulers, of whom 9 were kings, 2 were queens, and 2 were joint-kings. The most notable of these were the king, Thirumalai Nayak, and the queen, Rani Mangammal.
Context: Early in the 14th century, a dispute arose over the succession to the Pandya throne. One claimant appealed for help to emperor Ala-ud-din of Delhi, who dispatched his general, Malik Kafur, in 1310. Malik Kafur marched south, ransacking kingdoms on the way and causing enormous changes to the political configuration of central and Southern India. He marched into Madurai, sacking the town, paralysing trade, suppressing public worship, and making civilian life miserable. The great Meenakshi temple with its fourteen towers was pulled down, destroying the nearby streets and buildings, and leaving only the two shrines of Sundaresvara and Meenakshi intact. The events are controversial: as another account describes them, ...the Deccan was soon to feel the force of Islam, which was already the master of Northern India. In the reign of the able sultan of Delhi, Ala-ud-din Khalji (1296--1315 AD), a series of brilliant raids, led by the eunuch general Malik Kafur, a converted Hindu, crushed the Deccan kingdoms, and for a time a sultanate was set up even in Madurai, in the extreme south. Malik Kafur returned to Delhi following these events. The Pandyas protested the invasion, which continued for a few years in spasmodic fashion. The weakness of the Pandya regime caused the neighboring Chera ruler to invade and defeat the Pandya ruler, and he crowned himself in 1313. This was followed by a Chera occupation. However, the Chera occupation was transitory. A Sultan dynasty was soon re-established at Madurai, ruling Madurai, Trichinopoly and even South Arcot, for the next 48 years, first as feudatories of the Delhi Sultanate and later as independent monarchies. In 1333, during the rule of Muhammad bin Tughlaq, Jalal-ud-Din Ahsan Khan declared independence from the Delhi sultanate and ruled the area until he was killed by one of his officers in 1339. Alaud din Udauji Shah (1339-1340) took power in 1339, but soon met with the same fate. Qutb ud din Firoz took over in 1340 and was killed in about forty days. Giyaz uddin Muhammad Damghan (1340-1344) ascended the throne in 1340 and later married a daughter of Ahasan Shah. Ibn Batuta visited Madura during his reign and he testifies to his atrocious behaviour. He was defeated initially by the Hoysala Veera Ballala, but later captured and killed Ballala. He died in 1344. Nazir ud din Mahmud Damghan (1344-1356), Adl Shah (1356-1359), Faqr ud din Mubarak (1359-1368) and Ala ud din Sikandar (1368-1377) followed him in succession. When Sikandar was defeated by Bukka in 1377, the region became part of the Vijayanagara Empire. CANNOTANSWER
Question: how did he take over Madurai?

Answer:

crushed the Deccan kingdoms, and for a time a sultanate was set up even in Madurai, in the extreme south.