How do I get Ribbons?

Location of the Ribbons are as follows:

• Gaea's Cliff in a hidden passage (Disc 2)
• Temple of the Ancients in room V of the clock room (When accessible)
• By winning 10 Special Battles in the Gold Saucer at the battle square

Alternatively, you can get infinite more by morphing these enemies:
Master Tonberry (Northern Crater)
Ho-chu (Special Battle Square)

Also, it might be helpful to note that Yuffies ultimate weapon, The Conformer, does not take the morph damage reduction penalty, meaning she can still do 9999 damage with Morph. This allows Master Tonberries to be easily morphed.
It is also good to know that Master Tonberry can be located in the Nothern Crater Swamp area and has 44444 HP.

All information was taken from this guide.