If the computer can see the card (if you're running Windows, look in Administrative Tools/Computer Management/Storage/Disk Management - if the filesystem was destroyed, Windows itself won't see the card), it's trivial. Download
PhotoRec. With the card in th computer, try to follow the steps in
PhotoRec Step By Step (you'll be dealing with Linux naming conventions, so take your time if you're not comfortable in Linux). It can take hours to recover everything on a large card, so just let it run and check on it every half hour or so, in case there are any popups you have to answer.
If the files are still on the memory chip in the card (there's more than just a memory chip, it's a whole computer), PhotoRec will recover them.
If nothing can recognize the card, you can't recover the files. However, if it's a SanDisk card, go to
SanDisk Online RMA Request and fill out a request. At least you can get the card replaced. (And from now on, have anything important backed up off the phone.)