You didn't say which camera but most that I know of do a quick format which only resets the FAT, leaving the actual data on the card untouched.
Do a 'Google' search on 'file recovery software' for the platform you're using (PC, MAC, etc.) to see what's available. There are many out there - some free, some with a cost. All have different features.
Three that I've used in the past (although not very recently) are "PCI File Recovery", "Smart Recovery", and "Zero Assumption Recovery" - all for Windows.
Keep in mind that even if the files themselves are recovered the original file names may not be so identifying what you recover can still be challenging.