How should one resign properly? In some of the tournaments I've been to, there were pretty indecent people (some of whose licenses were revoked).
One of my friends had a terrible incident. At the end of the game, he was dominating and his opponent looked at him, told him that he resigned, they shook hands and reset the pieces. When the referee came, their opponent claimed that they agreed for a draw.
Even though the referees asked the other players, they just said they shook hands and reset the pieces together. Naturally, cameras showed the very same thing. At the end of the day, he was not able to prove the fraud and lost half a point from an already won game.
A similar thing might be observed at the end of Carlsen's defeat against Anand in Dubai. What prevents Carlsen from claiming that they agreed to a draw?
Moreover, unfortunately, these types of frauds do not only occur in local tournaments. For instance, there was the game Tal vs. Adamski where Tal's wife saved the day.
Thus, my question is somewhat two-folded. How should one resign properly, and proceed when the opponent tells that they resign?
In the USA, we have to notate our games. This would likely prevent issues where an opponent claimed a draw fraudulently.

I played tournament chess for years and never knew of a single instance of the sort of fraud and cheating that you mention.  (My point is that I have not had to deal with it so others may have more germane experience.)

EDIT - good observation by @ghotir.  If you agree to a result, write the result, sign the scoresheets, and do not reset the board until this has been done. Even so you both have the scoresheets.  That's how it happens at tournaments.