Current questions and answers regarding the map editor.

And if I want a certain hero to receive an artifact when the yellow player defeats the green player, how should I write that?
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Preparing the "Crushing" map for the dwarves. Map progress - 30%

If the green player is player number 3 and the yellow player is player number 4, you can do it like this (you can change the numbers if needed):

Trigger(PLAYER_REMOVE_HERO_TRIGGER, 3, "RemoveF");

function RemoveF(looser, winner)
if GetObjectOwner(winner)==4 then
GiveArtefact(winner, nArtID); --// nArttID - ID of the artifact, you can find it and other IDs in the Editor Documentation folder, in the HOMM5_IDs_for_Scripts file.
Trigger(PLAYER_REMOVE_HERO_TRIGGER, 3, nil);
end;
end;

Added 2 minutes later

What are the if-then, do blocks, and functions?

I already shared the Scripts document; everything is described in detail there