Firoz Shah Tughlaq was the third ruler of the Tughlaq dynasty of the Delhi Sultanate. He became the emperor after the death of his cousin Muhammad bin Tughlaq. Here is how he became the emperor:

Ascension to the Throne
1. Death of Muhammad bin Tughlaq: Muhammad bin Tughlaq died in 1351 after ruling the Delhi Sultanate for 26 years. He did not have any heir to succeed him.
2. Claim to the Throne: Firoz Shah Tughlaq was Muhammad bin Tughlaq's cousin and the son of Rajab, who was the younger brother of Ghiyasuddin Tughlaq (Muhammad's father). Firoz Shah claimed the throne as the next-in-line to the Tughlaq dynasty.
3. Support from the Nobles: Firoz Shah had the support of the nobles and courtiers of the Delhi Sultanate, who saw him as a capable and just ruler. They helped him in his claim to the throne.

Consolidation of Power
1. Challenges to the Throne: Firoz Shah faced challenges to his throne from his own family members, who were also claimants to the throne. He had to suppress their rebellions and consolidate his power.
2. Administrative Reforms: Firoz Shah introduced several administrative reforms to strengthen his rule. He reorganized the revenue system, improved agriculture, promoted trade and commerce, and established hospitals and schools.
3. Military Campaigns: Firoz Shah also undertook military campaigns to expand his kingdom and consolidate his power. He defeated the neighboring kingdoms of Bengal, Orissa, and Jaunpur.

Conclusion
Firoz Shah Tughlaq became the emperor of the Delhi Sultanate after the death of his cousin Muhammad bin Tughlaq. He had the support of the nobles and courtiers of the Delhi Sultanate, who helped him in his claim to the throne. Firoz Shah also had to face challenges to his throne from his own family members, but he consolidated his power through administrative reforms and military campaigns.

Firoz Shah Tughlaq was the third ruler of Tughlaq dynasty that ruled over Delhi from 1320 to 1412 AD. Tughlaq was in power from 1351 to 1388 AD.
He ascended the throne after the death of his cousin Muhammad-bin Tughlaq (ruled from 1324 to 1351 AD). The dynasty started from the rule of Ghiyasuddin Tughlaq (ruled from 1320 to 1324 AD) and ended at Nasiruddin Mahmud (ruled from 1395 to 1412 AD).