How to find save files for FFVII | Originally a post by @Fawkes

First locate your FINAL FANTASY VII install folder. This is usually at C:\Program Files (x86)\Steam\steamapps\common\FINAL FANTASY VII

But if you have used 7H before, chances are your FF7 folder is elsewhere. So open 7th Heaven. (If you don't know where that is installed, try to look for 7th Heaven.exe throughout your whole Drive). In 7H go to Settings > General Settings and you should find the location of the FINAL FANTASY VII folder.

Now your saves can possibly be at one of two locations. These are:

...\Documents\Square Enix\FINAL FANTASY VII Steam\user_<your square-enix user ID>
...\Steam\steamapps\common\FINAL FANTASY VII\save

The former is used for Square Enix's cloud save feature.
The latter is used when playing using 7H. So now you know where to expect your saved games to be and where to put them if you are copying them from elsewhere, depending on how you are starting the game.

Inside these folders there should be files named like saveXX.ff7 where XX is the save group number. This file is the actual save data and should be placed in the right folder for them to show up in-game.

By Fawkes