Initial Love Points:

Aeris: 40
Tifa: 30
Yuffie: 20
Barret: 10

You have to get more points with the one you want to date by being as nice to tthem as you can, while also losing points with the others. In case of a tie, It will go in order of initial (i.e. if Tifa and Barret both have 98 points, and the others have less than 98 points, then Tifa will go out with you). I think there's a guide of this somewhere on GameFAQs. I'm pretty sure that's where I found it, and that's where I got my information, by the way. Also, according to said guide, actions in battle make no difference, but who you choose to battle in event driven party changes (like when you're on the boat for the first time and Yuffie asks to be left out 'cause of motion sickness), those do effect the Love Points.