Keep in mind that it's based on the Japanese version of the game, so
the conversations/events may seem a little different.  Also credit is
also given to the original writer of this guide, since it was translated
from Japanese into English:

GENERAL TIPS FOR DATING YUFFIE
written by ????

 - Always have Red 13 + Barret in your party before getting Yuffie.

 - After getting Yuffie, make sure she's always the second character,
   unless specified otherwise, (like when a character insists on
   joining you).  The third character can be anybody but one of the
   girls (unless specified otherwise).

 - When you talk to allies, always talk to Yuffie first.

 - If in doubt when making choices, remember the object is of getting
 - Tifa/Aerith's favour of you down (that is, be nasty to them), and
 - getting Yuffie's favour of you up.

 - Finally, make sure the Cover materia is always equipped on Cloud when
   Yuffie's in your party, so that he can protect her.

 - Below is what choices you need to make to date Yuffie - don't be
   daunted by the number of instructions. This is partly in shorthand
   because I only got them from my Japanese friend on the phone. Good
   luck dating Yuffie!

1.  When you meet Aeris, tell her not to worry.
2.  then 'ah, nothing.'
3.  want/don't want flower, say 'don't want'
4.  when talk to Jessie in train, choose 'I'll be waiting'.
5.  In front of 7th Heaven, don't talk to Barret.
6.  With Tifa's speech (Did you fight with Barret?) say 'I didn't'.
7.  When talk to Biggs (about food), say 'yes, okay.'
8.  When talk to Wedge, don't choose 'I'm not interested.'
9.  When talk to Tifa at bar, say 'I don't feel like it.'
10. In Avalanche hideout, after talking to Barret and then
    talking to Tifa, choose '....sorry.'
11. then, when Tifa says, 'Did you sleep well,' say 'Barret
    snores a lot'.
12. When Barret asks about materia, say 'I'll explain to you.'
13. In Johnny's house, when talk to J's father, say 'I don't
    care about my hometown,' not 'Nibelheim..'
14. When in train to attack second mako reactor, Jessie says
    'do the clothes suit me?' say, 'yes, it does'
15. when falling from bridge, say to Tifa, 'I mightn't be able
    to make it,' not 'I'm gonna try to hold on.'
16. When Aerith says 'do you remember me?', say 'This is the
    first time.'
17. When Aerith says 'I've got a lot of things to tell you, don't
    say 'Okay, I'll listen,' instead say, 'there's nothing to talk
     about.
18. When Reno enters and Aerith says, 'Ignore him,' talk to Reno.
19. When Aerith is attacked, and she says 'Cloud, help me,' say,
    'wait a minute', and drop all the wrong barrels.
20. At Aerith's house, when Aerith's mom says, 'Are you her
    girlfriend?', say, 'Yes, I am'.
21. At park, when Aerith says, 'I don't want to go home,' say
    'I'll take you to 7th Heaven'.
22. Don't go to the brothel in the wall market and try to make
    Aerith be chosen (only three dress-up items).
23. When in Don Corneo's house, say when you save Tifa, 'Let's
    go and save Aerith,' not 'Are you alright?'
24. At sewer after boss, talk to Aerith then Tifa.
25. When you talk to Marlene at Aerith's house, and she says,
    'Is Aerith your girlfriend?' say 'I don't know.'
26. In front of Shinra building, choose 'Let's go straight in'
    (agree with Barret).
27. At 61st floor, talk to guy who has keycard to the 62nd
    floor, and say first, 'Where's Aerith?' and then, '....'.
28. At 68th floor, when you first save Aerith and you get to
    choose who takes Aerith away, say 'Tifa, I'm counting on you.'
29. In jail, talk to Red XIII first,
30. then talk to Barret,
31. then talk to Aerith,
32. then talk to Tifa. When Tifa says, 'Can you get us out of
    here,' don't choose 'Leave it to me,' choose 'It'll be difficult.'
33. And then go to sleep.
34. Before bike race, in your party to fight bulldozer boss, have
    Red and Barret in your party.
35. Talk to Red first when you escape.
36. Then talk to Barret, and say 'I'm not sure.'
37. Then when talking to Tifa and Aerith, say 'The journey's going
    to be dangerous, is that alright with you?'
38. When choose members, have Red+Barret.
39. In KaLm and flashblack, say you did go into Tifa's house.
40. Say you did go into Tifa's room,
41. Say you looked at Tifa's letter on desk
42. Say you read it.
43. Say you remember it very well.
44. Look at drawers, and then say 'Yes, I really look in your
    drawers.'
45. After flashback, when talking to Barret about him wanting to
    go off and fight now, say 'Is that all?'
46. After going through Mythril mine, go and get Yuffie straight
    away (before going to Junon). Helps if you're got a high level.
47. In front of Condor fort, with PHS, make members, Aerith and
    Tifa.
48. After going inside, talk to guy sitting, holding his head,
    choose 'I'm not interested.'
49. Go outside, with PHS, make members, Yuffie/Red, and then go
    in and talk to same guy and say, 'I accept.'
50. After someone says in Condor Fort, 'Are you going to rest?'
    say 'I want to rest', not 'not yet.'
51. In Junon, if you don't have 'Tranquilizer', buy some.
52. In cargo ship, talk to Yuffie, and she talks about 'Tranquilizer',
    say, 'I'll use it.'
53. When Aerith says, 'The Airship is wonderful, isn't it?' say
    'Oh, I don't know,' not 'I'll let you on one day.'
54. Tifa says, 'When war ends, etc.', say not 'Yes,' but 'I dunno.'
55. When make up party, use Yuffie+Red.
56. When go to Costa del Sol, go to beach, don't say, 'Hey that's
    Hojo,' say, 'Who, that girl in the bikini...?'
57. In inn, talk to Aerith lying in bed, when she says, 'what do
    you think of me?' don't say, 'I don't know,' say, 'hmm.. not much.'
58. Go house next to bar, talk to Tifa who's talking to Johnny,
    when she says, 'don't worry', say 'I'm not worried.'
59. Talk to person on Corel path.
60. At save point on Correl railway, with PHS, make members
    Tifa+Aerith.
61. When you hear bird song, investigate the birds nest, say,
    'Take the treasure,' not 'Let's leave it.'
62. Straight away in North Correl, make member change to
    Yuffie+Red.
63. In talk before going on Ropeway to Gold Saucer, choose
    'Let's get on.'
64. In Gold Saucer, just talk to Yuffie and make her a part
    of the team.
65. In prison, because Barret must be in your party, make
    the party with Barret+Yuffie.
66. After escape from prison, make party Yuffie+Cait Sith.
67. At Gongaga, when with Reno+Rude, don't say 'Get outta
    my way,' say 'What's with you?'
68. Look at Scarlet and Tseng's conversation.
69. Go outside and change members to Aerith+Tifa.
70. Go to Zack's house, and when Aerith+Tifa leave you,
    ignore them and leave.
71. After out of Gongaga, make party Yuffie+Red.
72. At Cosmo Canyon, talk to Yuffie (she's in materia shop,
    suprise, suprise!)
73. In Planetarium, make Yuffie+Cait Sith in party.
74. Before Cosmo Candle, talk in this order: Yuffie, Barret,
    Aerith, Tifa, Red.
75. In Gi clan's cave, make party as Yuffie+Red.
76. At Nibelheim, make Vincent in your party, then talk to
    Sephiroth,
77. In Rocket Town, when get Tiny Bronco, listen to Yuffie when
    she says, 'Lets go to the west (to Wutai).'
78. At Wutai, Yuffie takes your materia. At this time, although
    there'll be less members, do not replace Yuffie.
79. After battle with Shinra Soldiers, make members Vincent+Cait
    Sith (maybe Cid+Red if you want).
80. At Wutai, when you've caught Yuffie, pull left lever as she
    says.
81. Finish Wutai events (inc. Pagoda with five bosses if you can),
    then go to Gold Saucer, get the Keystone, and watch the date
    sequence begin.

Congratu