In Farming Simulator 19, vehicles and machines lose their durability and efficiency. As for vehicles, you can easily check whether they are damaged or not - this is presented in the bottom right corner, above the speedometer. As for machines, you have to check their status in the vehicle overview screen.
To repair a vehicle or a machine, open the owned items screen and select an item you want to repair.
Repairing in the workshop behind the shop
However, you can pay less for repairing by going behind the shop and reaching the zone where you can modify/sell items.
Repairing in your own workshop
The game gives you the option to build your own workshop. Go to Shop -> Placeables -> Miscellaneous -> Vehicle Workshop. This buildings cost $28,000. However, it allows you to repair and modify vehicles in your parcel.