Instructions
Install "Trackmania Nations Forever."
Find and download your desired car. There are a few websites where you can do this, and the most popular one is Trackmania Carpark.
Enter your Trackmania directory. By default it's "C:\Program Files\TmNationsForever\GameData\Skins\Vehicles"; if you got the game from the digital distribution system "Steam," your Trackmania directory is "C:\Program Files\Steam\steamapps\common\trackmania\GameData\Skins\Vehicles".
Select the "StadiumCar" folder and press "Ctrl+C" then "Ctrl+V". This will create a backup of the folder and allow you to restore any of the game's original cars.
Double-click the "StadiumCar" folder and select any one of the files inside. Right-click the selected file and click on "Rename". Press "Ctrl+C", then "Enter", and delete the selected file.
Move your downloaded car file into the "StadiumCar" folder, select it, right-click, and click on "Rename". Press "Ctrl+V", then "Enter". Your downloaded car will have a new file name. Write the name down.
Start your "Trackmania Nations Forever" game. Select "Profile" from the game menu, then click on "Vehicles". Find the name of the car you wrote down, which will be the car you downloaded.