Optional step zero: Take a headache pill. Then go through the steps below until finding a way to continue. Most such cases will be due to confusion. Sometimes it is deliberate on the part of one person.
Step one: See if they can agree on the last position.
If so then continue with that and you are done. A common error is one person thinking that the opponent was checkmated while the other player sees a winning position if there is no checkmate. Example: one player plays Qg6+, says mate and starts sticking out a hand; the other player captures the queen and shakes the hand thinking the player is resigning.
Step two-A: See if you can reach a position they do both agree on and continue from there.
or
Step two-B: The simplest course may be to accept the one the player with a significantly weaker position gives and play on from there even if the other player didn’t give the same position. Often the other player will look at it and accept it after seeing a way to win and the player whose position you chose was given the full benefit of any doubt.
Step three: Go with your best judgement about what the position was.
Step four: Play a new game or rule it a draw. I detest doing this and have done it maybe twice in the past two+ decades (figure in excess of 400 tournaments).
Note: If you do continue the game then see if you can assign a witness to watch what happens (preferably a TD but I have used non-TD witnesses after giving both the witness and the players explicit instructions that the witness cannot say anything or make any rulings but is only there in case a TD needs to find out what happened - this is one case where I’d accept using a camcorder or cell phone video to track the game).