To recover data from a formatted hard drive or SD card manually, start by checking the Recycle Bin for any accidentally deleted files. If they’re not there, use built-in system utilities like Windows' "Previous Versions" or macOS's "Time Machine" if backups were made. For a more comprehensive recovery, employ a data recovery tool like BLR Data Recovery Tool. This tool scans the formatted drive or card thoroughly, detecting and recovering lost files that manual methods might miss. It supports various file systems and ensures a higher recovery rate, making it a robust solution for retrieving valuable data.