Cloud You must earn 32000 points in the Battle Square.
Barret After the train ride into North Corel,talk to the women in the house just south of the inn
Tifa Play the Melody from Cloud's flashback in Kalm Town on the Pianoat Tifa's in Nibelheim.The melody is: Do Re Mi Ti Fa Do Re Mi So Fa Do Re Do. If you have learned all of her other moves you will get the manual.
Aeris If you have between six and seven hundred battles,visit the sleeping man in the cave east of Junon and he will give you some Mithril. Take this to the blacksmith who lives East of Gongaga, then oper the upstairs hatch to get the Manual.
Red XIII You'll get this for defeatind Lost Number, the boss in the safe in Shinra Mansion.
Yuffie If you defeat the Tower of The Five Gods you'll get her Manual.
Cait Sith There is no manual for Cait Sith