Here's how to get the best ending.

1.When Asuka is coming towards Shinji, answer "It isn't the case, Kensuke" (second choice)
2.Answer the first choice
3.Answer "Look at the transfer student" (first choice)
3.Answer "Look at the transfer student in the swimming pool" (second choice)
4.During the pause, answer "Go to library" (first choice)
5.In the library, answer "Help transfer student to pick up books" (second choice)
6.Answer the first choice after touching Mayumi's hand.
7.In the Entry Plug, answer "Looking at Misato" (third choice)
8.Answer "Fight short range attack" (first choice)
9.Purposely lose to the enemy in this battle, then you will automatically detect the presence 10.of transfer student and will automatically pick her up. After picking transfer student up,defeat the Angel.
11.Answer "I understand" when Misato tells you to go to school (second choice)
12.When you are in your bed, answer "I cannot forget today's battle" (first choice)
13.Then answer third choice If everything is correct, Shinji should think of the transfer student instead of his father when he turns to the side.
14.In the morning, answer "Go to NERV HQ" (first choice)
15.When you meet the transfer student, answer "You really like books a lot?" (sorry, cannot remember which choice it is)
16.Answer "I frequently read books" (second choice) If everything is correct, you shall see Mayumi feeling throbbing sound in her stomach.
17.In the classroom, if Asuka tells you to answer for her, answer the third choice. You may have Shinji being tested; in this case, you have nothing to do, Mayumi will answer for you.
18.When Touji and Kensuke ask you to choose a singer, answer "Invite Mayumi as singer" (first choice)
19.Answer the second choice. Mayumi should join you. After that, you will see Mayumi dreaming.
20.Answer the first choice when Asuka says she can defeat the Angel all by herself.
21.Choose "Long range attack" (second choice) If everything is correct, the Angel should attack the school during the battle.
22.In the anime scene where Shinji is waiting for repairs, Mayumi will come to Shinji, and tell him to kill her; answer the first choice. During the battle, you will see Mayumi trying to commit suicide.