Rewatch the movie or read what Kevin, Martok or Jim have written. If you want my version in a nutshell:
Impulsive Kirk naturally dislikes rational Spock and vice versa, Spock maroons Kirk, PrimeSpock tells Kirk that they have to become friends (causality paradox ?!), Kirk provokes Spock and shows him his human side, Spock learns from his father that emotions can be an asset, Spock wants to help and Kirk accepts him, they go on a mission together and start to get along, they learn to appreciate the strength of each other's styles, they develop mutual respect ... and at the end of the flick you can easily extrapolate that they might soon become good friends.