the memory cards all function the same and are still interchangeable, they're all just titled under their specific game now. you play FF8, you can take that memory card, rename it to a (say) Legend of Mana memcard, and you can use it to get your chocobo pet (it's a legend of mana thing).
so basically, just take the memory card with the saves that you need, and rename it for the game you're about to play. don't forget to move the memcard to that game's folder.
as far as using saves with multi-disc games (FF7, FF8), there's an option where you can "insert new disc" from (say) the first disc. it's in the options somewhere. i usually just put each disc of a game under different folders (FF7 Disc 1, FF7 Disc 2), but keep each disc's BIN file the same name (FF7.bin, FF7.bin) that works too. as long as the names match, it's just like a real memory card in the real PSX.
some games like Xenogears have an in-game menu where you can move and copy save files. i have a dexdrive, but i still find that menu pretty damn useful.