2.) Check the Point Release(abbreviation for Point Release is P.R.) on the bottom of the Demo Download, i will only put up Point Releases 1.16 and 1.31 Demos.
3.) Download the demo, and unzip the file.
4.) Whatever the file is(say it is 1.16), open up your 1.16 baseq3 folder and make a folder in there called, "demos" (with out the quotes and it has to be all lowercase).
5.) Drag the demo file into the "demos" folder, and exit out of there.
6.) Open up your 1.16 Quake 3 and when in the Main Menu click on DEMOS then it should be there.
***Reminder***
1.31 File Extensions are: DM_67
1.16 File Extensions are: DM3
DM3 files will not work with any other Point Release other than 1.16
DM_67 files will not work with any other Point Release other than 1.31
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If I did not clearly explain everything in a understandable way, then post on the Forum.
-Carnage