In general, if you want to play a map using a mod, you move the map file to the mod's directory.
e.g., into quake/coppper/maps/ from, say, quake/dopa/maps
The issue is that if it has any features that copper doesn't support, those elements will not show up. So in the case of Dimension of the Machine, Chthon will be MIA (or invulnerable) in Copper, and the dynamic lights will be no doubt missing as well.
Unlike what u/newsflashjackass says, you CAN move things to copper mod in Kexquake. Don't listen to them, they're spouting bullshit. Kex runs tons of various mods, including Arcane Dimensions (though one map, Tears of the False God, won't run due to limitation issues that has nothing to do with format as they claim), and even actively has a version of Copper in its add-ons.