It's fairly convoluted, but not that difficult once you get a grasp of the material.
In the Lifestream sequence, we see the young Cloud having trouble "fitting in,"
Quote:
Kid Cloud: Tifa always used to be with this three-some.
Tifa: ...That's right.
Kid Cloud: I used to think... they were all stupid.
Tifa: What!?
Kid Cloud: You were all childish, laughing at every little stupid thing.
Tifa: But we were children, back then.
Kid Cloud: ...I know. I'm the one that was stupid. I really wanted to play with
everyone, but I was never allowed into the group. Then later... I began to think
I was different... That I was different from those immature kids. That then...
maybe...
Shadow Cloud: Just maybe, they would invite me... I thought that might happen,
so I hang around...
Kid Cloud: I was so prejudiced. And... weak.
...as well as being unjustly blamed for Tifa's injuries after they fell at the beginning of Mt. Nibel, yet blaming himself for being unable to save her.
Quote:
Kid Cloud: Tifa was in a coma for seven days. We all thought she wouldn't make
it. If only I could've saved her... I was so angry... Angry at myself for my
weakness. Ever since then, I felt Tifa blamed me... I got out of control... I'd
get into fights not even caring who it was. That was the first time I heard
about Sephiroth. If I got strong like Sephiroth, then everyone might...
Shadow Cloud: If I could get stronger...... Then even Tifa would have to notice
me......
As a result, he attempted to join SOLDIER. However, he didn't succeed (I believe the reason he didn't get in was primarily due to the requisite JENOVA therapy, compounded by his own doubt).
Two years later, Cloud (a grunt soldier for Shinra) accompanied Sephiroth and Zack (the "black-haired member of SOLDIER) to Nibelheim. SOLDIER had been called in due to a spike in monster activity. Having not made SOLDIER, Cloud was ashamed and did not reveal his identity to Tifa. After Zack and Sephiroth investigated the reactor and found the problem (Hojo was basically responsible), Sephiroth began to question his own identity.
Quote:
Cloud: Wh... what is this!?
Sephiroth: Normal members of SOLDIER are humans that have been showered with
Mako. You're different from the others, but still human. But, what are they?
They've been exposed to a high degree of Mako, far more than you.
Cloud: ...is this some kind of monster?
Sephiroth: Exactly. And it's Hojo of Shinra that produced these monsters.
Mutated living organisms produced by Mako energy. That's what these monster's
really are.
Cloud: Normal members of SOLDIER? You mean you're different? H... hey,
Sephiroth!
Sephiroth: N...no...... ...Was I?
After repeatedly striking the capsules with the Masamune, Sephiroth continued.
Quote:
ephiroth: ...Was I created this way too? Am I the same as all these
monsters......
Cloud: ...Sephiroth.
Sephiroth: You saw it! All of them... were humans...
Cloud: Humans!? No way!
Sephiroth: ...I've always felt since I was small... That I was different from
the others. Special, in some way. But... not like this...
After reading up on the Jenova Project in the basement of the Mansion, Sephiroth apparently came to believe that JENOVA was actually an Ancient, and that normal humans had essentially usurped Gaia from the Cetra. He proceeded to go on an utter rampage, leaving Nibelheim in flame and most of its residents (including Cloud's mother and Tifa's father) dead. Sephiroth returned to the Mt. Nibel reactor for the body of JENOVA; Cloud, Zack, and Tifa independently followed. There, both Zack and Tifa were struck down by Sephiroth when they confronted him. Both were gravely wounded by the slashes, but neither died. Cloud picked up Zack's Buster Sword and struck Sephiroth, but Seph was able to rip away the Mechanical Angel, and limped off with the head of JENOVA. Cloud (who had briefly looked after the unconscious Tifa) followed, but was impaled (apparently through the shoulder) by the Masamune. Somehow, Cloud was able to take the Masamune by the blade and hurl it and its wielder into the depths of the reactor.
At this point, Shinra began to stage a cover-up of the disaster. The town was rebuilt and populated by Shinra employees. Tifa's martial arts instructor, Zangan, was able to saver her and take her to Midgar, but Cloud, Zack, and the surviving residents (these residents were the black-garbed CLONES that followed Seph to the Reunion, by the way) were captured and used by Hojo in various JENOVA cell experiments.
Eventually, Zack and Cloud were able to escape. Zack, a member of SOLDIER, had exhibited no reaction to Hojo's Mako and JENOVA cell experimentation. Cloud, however, had reacted to the JENOVA cells, and was barely conscious.
(Taken from the Escapee Reports in the basement)
Quote:
Escapee report no. 2
Description at the time of capture.
A - Former member of SOLDIER/Number ( )
No effect could be detected from either Mako Radiation Therapy or Jenova on him
B - Regular/Number ( )
Reaction to Jenova detected.
Zack and the barely aware Cloud began travelling away from Midgar. Zack related a number of his memories to Cloud. Just outside Midgar, Shinra caught up with the two and gunned down Zack. They didn't kill Cloud, however, as he was in a completely helpless state. Cloud managed to drag himself to the Train Station, where he was found by Tifa. By now, Cloud had begun to mix up his own memories with Zack's, effectively superimposing himself over Zack during the Nibelheim disaster (the final transition of memories is indicated by the flashing screen in the flashback).
Cloud firmly believed in his altered memory of the disaster, but Tifa had seen Zack, not Cloud. Hence, she was very confused as to how Cloud knew certain things when he had not been present (as far as she knew).
Eventually, the party pursued Sephiroth to the Whirlwind Maze. There, he was able to completely screw with Cloud's mind, since the superimposition of himself over Zack in the memory led to some innconsistencies. Sephiroth was thus able to convince Cloud that he was constructed five years earlier.
Quote:
Sephiroth: Ha, ha, ha...... I want to take you back to your real self. The one
who gave me the Black Materia that day... Who would have ever thought a failed
experiment would prove so useful? Hojo would die if he knew.
Cloud: Hojo!? What does he have to do with me!?
Sephiroth: Five years ago you were... ...constructed by Hojo, piece by piece,
right after Nibelheim was burnt. A puppet made up of vibrant Jenova cells, her
knowledge, and the power of the Mako. An incomplete Sephiroth-clone. Not even
given a number. ...That is your reality. Ha, ha, ha......
Convinced of this, Cloud later related his false status as a failed Sephiroth clone to Hojo later on in the Maze.
Eventually, though, Tifa was able to help Cloud break through the barrier he had established and remember the truth of his identity. After this (the Lifestream incident), Cloud effectively summed up his true identity for the party.
Quote:
Cloud: I never was in SOLDIER. I made up the stories about what happened to me
five years ago, about being in SOLDIER. I left my village looking for glory, but
never made it in to SOLDIER...... I was so ashamed of being so weak; then I
heard this story from my friend Zack... And I created an illusion of myself made
up of what I had seen in my life...... And I continued to play the charade as if
it were true.
Barret: Illusion, huh...? Pretty damn strong for a llusion, I'd say.
Cloud: I'm physically built like someone in SOLDIER. Hojo's plan to clone
Sephiroth wasn't that difficult. It was just the same procedure they use when
creating members of SOLDIER. You see, someone in SOLDIER isn't simply exposed to
Mako energy. Their bodies are actually injected with Jenova cells...... For
better or worse, only the strong can enter SOLDIER. It has nothing to do with
Jenova Reunion. But weak people...... like me, get lost in the whole thing. The
combination of Jenova cells, Sephiroth's strong will and my own weakness are
what created me. Everyone knew that. I'm...... Cloud. ......the master of my own
illusionary world. But I can't remain trapped in an illusion any more...... I'm
going to live my life without pretending.
Basically, exactly what happened can be derived froman examination of the Kalm flashback, the (pivotal) Lifestream incident, and the Zack/Cloud escape flashback which can be seen on Disc 3 when the party returns to the Mansion basement.
In summation, then, Cloud did not make SOLDIER. His friend Zack did. After both were captured by Hojo, the combination of JENOVA cells and Cloud's own self-doubt effectively weakened his own awareness, allowing for him to mix up Zack's role with his own. The resulting inconsistencies were manipulated by Sephiroth, but Cloud eventually regained his memory.
As to Tifa, she didn't die from the sword stroke, and was cared for by Zangan.
I think that covers everything; I'll be glad to explain anything further if some of what I posted is confusing.