The multishine is when you shine, start to jump out of it, and within the first 3 or 6 (someone correct me) frames that falco is still on the ground, you shine again. (shine, push y/x, immediately shine again)
the main use for it is if you shine someones shield and they try and grab you after it, you can shine again and get them. it's also used for flashyness because its pretty tough to do.
you don't really need to do it more than twice, unless you like being flashy
ask shiz for more info, he's an expert on multishining and he has a thread about techniques and stuff on the falco forum. if you scroll through those pages you'll probably find what you're looking for.
good luck
Note: double shining on the ground withou hitting anything has a different timing then double shining agaisnt a shield or a character, so get used to both. double shining on the ground, you have to moev your finger from jump to shine faster. when you hit something there's a few more frams to do it