When you go to 'Workshop' tab for the game and find a car you want, just hit the 'Subscribe' button and steam downloads / installs it for the game. Now the catch is, the mod is subject to change if mod author makes changes in Workshop or if it gets taken down. That's cuz the mod car doesn't go into the game's 'cars' folder. Instead it goes into steams Workshop \ Content folder under a folder named '645630' and the mod car will be under that in a numbered folder. So, if you wanted to play with Steam in 'Offline' mode and / or never worry about the mod going missing, you'd have to copy / move that numbered folder into the games 'Cars' folder and then rename the numbered folder to the actual cars name.

You'd just look inside it and copy the name of the car's *.cms file and rename the folder to that. But, you don't include the first part of the name... 'car_' or the last part.... '.cms'
For example, one of my mods has the file in it named... car_57belvedere.cms
So, I'd rename the folder to; 57belvedere
It is case sensitive btw.
This ensures the mod car will be recognized in all aspects of the game....such as if you wanted to use Liveries for that car.

Once all that's done, you'd want to go back into 'Workshop' and choose to show 'Subscribed' items. Then, favorite them if you hadn't already--this makes it easier to know which mods you had installed--and 'Unsubscribe' the mods. Now, you're all set for playing the game with Steam in Offline mode without your save getting corrupted cuz of 'Missing' cars if / when a mod gets taken down from Workshop. Believe me....it's happened plenty of times.