GOLD SAUCER
There are four values in the game, deemed "Affection values" in this guide. Realize that in no point during or in FF7 are there any explanations of anything below. It's extra stuff that you need to know though. At the start of the game, the values are set as:
Aeris: 50
Tifa: 30
Yuffie: 10
Barret: 0
As the game proceeds, certain decisions you make or tasks you do will change these values. When you reach the Gold Saucer Date sequence, which is unavoidable and comes at a specific time, whoever has the highest Affection value will be the one Cloud goes on a Date with. If, however, there is a tie for the highest, then the priorities are:
Aeris > Tifa > Yuffie > Barret
(so if Tifa and Yuffie tied for the highest value, and both had 45, Barret and Aeris having values lower than 45, then Tifa would be the one that Cloud would go on a date with.)
Basically, focus on Tifa for dating her, answer any questions by sort of ignoring the other characters. If you really want the specifics, here they are to help you understand.
Midgar
Talking to Aeris the first time, no matter what you say (believe it or not),
has no effect. Buy the flower, unless you want to date Aeris or Yuffie.
Talk to Jessie twice on the train home from the first mission:
"Thanks anyway" --
"Looking forward to it" (-3 Tifa)
When you enter Seventh Heaven, and you have a flower:
"Give it to Tifa" (+5 Tifa)
"Give it to Marlene" (+5 Barret)
If you talk to Tifa while she's behind the bar:
"I don't feel like it" --
"Give me something hard" (+5 Tifa)
When Tifa accuses you of leaving your childhood friend:
"How can you say that!" (+5 Tifa)
"...Sorry" --
When Tifa asks how you slept:
"Next to you, who wouldn't?" (+5 Tifa)
"Barret's snoring kept me up..." (+5 Barret)
Giving Barret a Materia tutorial has no effect.