Selphie first meets Squall by running into him when she is late for class; later on the same day, she is asked to deliver a message to his squad during the SeeD field exam in Dollet, thus becoming a party member. They pass said exam together and are eventually assigned the same first mission: to help the Forest Owls resistance group in Timber.
Selphie has a lot of patience towards Squall; she forgives his mistakes easily and tries to be as understanding of his reasons as possible. Still, not unlike the other party members, she has no problem putting him in his place when he needs to be brought back to reality (such as when he wasn't very inclined towards sending a group to the Missile Base, or when he was going to leave Rinoa to die during the Galbadian attack
WTF SQUALL, this is why you'll never have a wife). It seems that Selphie is rather fond of Squall; she admires and respects him greatly as a leader, accepts him as he is and consistently attempts to figure him out, her support being more inconditional than most people's. Throughout the game, she often tries to bring down his defenses, but, contrary to Rinoa, fails miserably, only causing him severe awkwardness ("Squall, why did you go on your own? Is Zell that important to you?"; "Squall! You big stud!"). All in all, she clearly considers herself a friend rather than a mere follower, and always acts as such.
Matters are obviously harder to interpret on Squall's end of the deal, what with him being aloof and fearful of attachment and loss. Still, he does loosen up quite a bit throughout Final Fantasy VIII, mostly thanks to a lot of support and attention from his fellow SeeDs and, of course, Rinoa. As for Selphie, he finds anyone who attempts to approach him an annoyance, and she is no exception, often leaving him embarrassed with her direct, honest remarks. However, he shows that he cares when he gives in to her, allowing her to go to the Missile Base, and later tries to cheer her up
(the key word being "tries") at Irvine's request – which means a huge deal coming from Squall. Eventually, he takes her to Trabia Garden, too, understanding her need to visit, despite it being out of the way. In addition to this, he seems to trust her as a fighter, leaving a lot in her hands during the aforementioned mission at the Missile Base.
In conclusion, and though he would never openly admit it, Squall cares about Selphie's safety (just as he does everyone else's), and is a friend to her in his own weird way.