Basically, after defeating Ultimecia, time started to de-compress. This opened up the possibility for the party to will themself back to their own time again, as you see Selphie and Quistis etc. doing after the battle. However, for this to work, it is essential to have faith in others (as Laguna explains before disc 4, it's all about love, friendship and courage etc.). Squall does NOT have faith in others, due to his continued inability to rely on anyone but himself (ie. his 'lone wolf' attitude).

Because of this, Squall's attempts to get back don't work, and after first going to the Orphanage, he ends up getting lost in a time warp of sorts. This time-warp reacts to his thoughts, emotions and memories (again, like Laguna talks about), which explains the landscape he's in; he thinks he's completely lost and alone, so the time warp looks like a vast, barren landscape. Then he gives up, and think's he's stuck for good, and the time warp now looks like a tiny island from which there is truly no escape.

Finally, his thoughts turn to Rinoa, but since his emotions are all messed up, the time warp only shows twisted images of Rinoa. All this stress and despair eventually leads to him collapsing. Now, there's no way of telling exactly what happened to him (did he faint or die?), but in the end it doesn't matter, because Rinoa (using her love towards Squall) is able to find him, awaken him, and together (using the 'power of love') they break free of the time warp and end up back in their own time.

I would say Squall merely fainted, because that enables Squall to have been woken up merely by Rinoa hugging him, but one might speculate that Rinoa's powers woke him from the dead.