Basically, save your game, make a backup, boot the game again, save right away, make a backup again. Rinse and repeat a number of times. Basically, make multiple savegame backups with only minor differences. Don't move your character. Don't collect any money. Try to make backups that are nearly identical to each other.
Then compare all those backups in a hex editor of your choice and you should find a 16 or 32 bit value, different in each backup, probably near the beginning or end of each backup, which can't reasonably be associated to a time stamp or something. That might be your checksum.
Then you'll have to figure out how the checksum is calculated. For that, it should help if you have knowledge about the overall structure of the save file. Usually, checksums are calculated over a specific range within the save file, usually disregarding some sort of header or the like. Try some common checksum algorithms, with different sectors of the files. Hex Workshop is a great tool for that.
It's not a straightforward process. Every game is different. Good luck.