N researched the past, so much of his conclusions match L's, so I will start from the beginning as to why N (and L) thought Light was the killer.
- Chapter 2/Episode 2 (19:11): The killer must be in the Kanto region.
- Chapter 3/Episode 3 (3:35): The killer must be a student.
- Chapter 4/Episode 3 (10:40): The killer must be a relative of the police.
- Chapter 11/Episode 6 (8:45): The killer acts alone and must be among those investigated by the FBI during the first 5 days.
- Chapter 15/Episode 8 (5:58): The killer was investigated by Raye Penbar and is thus part of Chief Yagami's family or part of Sub-Chief Kitamura's family.
- Chapter 19/Episode 9 (15:35): L's gut tells him Light is the killer.
From this point onwards, L keeps suspecting Light, but could never find any concrete evidence proving this conjuncture. This was mainly due to the false rules put in by Light himself. If it was not for those rules, Light would have been convicted. Then in chapter 58/episode 25 (18:45) L dies and in chapter 59/episode 27 (1:25) N and M come into play and the cat-and-mouse-game starts all over again.
- Chapter 60/Episode 27 (13:22) (M): The killer must know about the abduction of director Takimura.
- Chapter 63/Episode 27 (20:27) (N): L is a fake and now called L2.
- Chapter 75/Episode 30 (1:44) (N): L2 is the killer.
- Chapter 77/Episode 30 (10:53) (M): N finds out one of the rules is fake by M.
- Chapter 78/Episode 30 (12:16) (N): The 13 day rule is believed to be fake.
- Chapter 79 (N): The rule is confirmed to be fake.
- Chapter 82/Episode 31 (13:27) (N): The killer must be the son of Chief Yagami, Yagami Light.
- Chapter 85 (N): It is confirmed that Light is the first killer and Misa is the second killer.
From this point onwards, N keeps suspecting Light, but again needed evidence to actually convict Light. It took N until chapter 103 to gain this evidence and he only got it by chance too.
- Chapter 103/Episode 36 (21:16): Light confessed
Victory is mine
- Chapter 103/Episode 37: Mikami calls Light a God (2:37), and the only name not written down is Light's (3:00)
This was considered enough evidence to convict Light and the game of the killer is finally over when Ryuk kills Light.