This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
All that you really need is a dress and a wig. First, go to the Honeybee
Inn and talk to the silver-haired man. Ask about Tifa. Then, go up to
Corneo's mansion and talk to the bouncer. After that, go to the clothing
store and talk to the lady there. She'll tell you that her father is
drunk at the bar. So, go there and talk to the man sitting near the
entrance. He'll ask you what types of cloth should be used in making the
dress. After he's done talking to you, return to the clothing store.
The man will give you a dress depending on what types of cloth you
picked out earlier. After Cloud tries it on, go to the gym and compete
against Big Bro's trainees. Depending on how well you did at the squats
game, you'll get a wig. At this point, you can return to the clothing
store, put on the items, and then go off to Corneo's mansion. However,
while you're still in your normal clothes, there are other areas to
explore and other things to get.
To get a tiara, go to the store that's closed at the north part of town.
Talk to the man there and agree to listen to his problem. Say you'll
help, then go to the inn and spend the night. Cloud will wake up in the
middle of the night and go to the vending machine. Buy an item, then go
back to the store the next day. Depending on the value of the item you
bought, the man will give you a type of tiara as a reward.
To get undergarments, talk to the fat man in the white shirt near the
bottom of the first screen. He'll give you his Member's Card. Now, go to
the Honeybee Inn and go inside. If you go into the upper-left room and
talk to the image of Cloud, you'll pass out, but Mukki will wake you up.
You'll be given the 'Lingerie' as a present. If you want the 'Bikini
briefs' instead, enter the lower-left room and agree to sit in the tub
with Mukki and his pals. After washing, he'll give you the 'Bikini
briefs' regardless of how you answered his questions. A woman in the
Honeybee inn will also put make-up on your face after you get one
undergarment or the other, but I don't think this has any great effect
on the game.
There's another undergarment called 'Mystery Panties'. The description
says that it has a 'childish design on the front'. I have no idea how to
get this item at the moment.
To get some cologne, enter the sushi bar, sit down, and order whatever
dish you like. After eating it, tell the chef that it's okay, and she'll
give you some Coupons. Go to the pharmacy and use the Coupons to buy one
of three items. Now, return to the bar where you found the owner of the
clothing store and try to enter the bathroom in the upper-left corner.
Choose to give the item you got at the Pharmacy to the woman inside the
bathroom, and she'll give you a type of cologne in return.
The more items you have and the better they are, the higher the chance
of Corneo picking Cloud as his bride.