Fulfill the following requirements to get the characters to join your party:

Garcia: Chapter 2 - Have Ross talk to him.
Ross: Chapter 2 - Have Eirika talk to him.
Colm: Chapter 3 - Have Neimi talk to him on Turn 2.
Lute: Chapter 4 - Visit lower-left house.
Joshua: Chapter 5 - Have Natasha talk to him.
Amelia: Chapter 9 - Have Eirika or Franz talk to her on Turn 5.
Gerrick: Chapter 10 - Have Innes talk to him.
Innes: Chapter 10 - Have Tana or Eirika talk to him.
Marisa: Chapter 10 - Have Gerik talk to her.
Tethys: Chapter 10 - Have Gerik talk to her.
L'Archel: Chapter 11 - Have Eirika talk to her.
Dozla: Chapter 11 - Have L'Arachel talk to him.
Ewan: Chapter 12 - Visit the small house on Turn 5.
Comrag: Chapter 13 - Have Eirika talk to him.
Rennac: Chapter 14 - Have Eirika or L'Arachel talk to him.