Each character has a certain list of other characters that it can share a support conversation with. This number can vary (Knoll has only 3, while others have as many as 8 ). Each character may only have 5 total supports within a single file. 2 characters may only share 3 supports with each other. Each time you use a support conversation, the 2 characters involved gain a bonus when they are within 3 spaces of each other. The bonuses have 4 individual buffs, which may include strength/magic, avoid, critical chance, critical avoid, etc. The bonus/buffs depend on each character's affinity. Secret characters (Riev, Valter, etc) have affinities, but said affinities are purely cosmetic. Secret characters can not have support conversations, which makes them inferior to normal characters. To get all support conversations, you must do one of two things. One, you could play through the game multiple times with different characters (very difficult and time consuming). Two (much easier), you could go to the Tower of Valni. Use the characters you want to support (temporarily). Go through the first 3 levels (or longer) and optimize your characters' supports. Then, reset your game, and restart the chapter. The character's won't keep the supports, but the conversations are saved in Extras, within the main menu.

Who you support permanently is your choice, but some supports may be better than others. Use this guide for advice on who to support with who. Credit goes to Holothuria, who wrote it.

http://www.gamefaqs.com/portable/gbadvance/file/921183/58848