The only thing I do when transferring SD cards (and I do it a lot) is to make sure that the device the card is coming out of or going into is turned off. You should be able to unmount the card, then remove it, and you should be able to insert it into a phone (or tab) that's turned on, but I don't like taking chances, and it only takes a minute to get the device running again.
As far as formatting or anything else, as long as it's standard format - FAT32 up to 32GB, exFAT for larger cards - it should work in any computer, phone or tablet.