Hey, hope I can help you. So the latest version of Warcraft III, which is as we may know, Reforged, does not support the custom campaign. The latest Warcraft III version that has a custom campaign is 1.31.1. While latest version generates significant amount of bugs, especially the unit event trigger and black screen bug, you can still play custom campaign assuming your Warcraft III version is not Reforged. You can download the older version of Warcraft III (not Reforged) using the link below.
WC3 Download Archive (1.00 - 1.31.1 + BETA & DEMO)
NOTE: You can also install multiple versions of Warcraft III by using the "Game Files" method.
After you do that, go to Documents folder and you will see a folder called "Warcraft III". In there you must make a new folder called "Campaigns". Put the custom campaign (w3n files) in there. For the older version of the game, the "Campaigns" folder is located in your game folder.
To play the game, make sure you start using "Warcraft III.exe", NOT the Launcher, and do NOT hit the Battle.net button. If you are using older version, you use "Frozen Throne.exe" instead. Anything that's related to Battle.net (like the Launcher or the button in-game) will update your game to Reforged. Go to "Single Player" -> "Custom Campaign" and then you should see your campaign. Select one and then click "Play Campaign" button.
If you still have trouble let me know, and let me know what your folders look like, and I will see if I can help more!