Barns - are unlocked after reaching level 6. After that, barns will appear on the map. There can by 20 of them tops. If you don't visit them, the new barns that would appear on the map with reaching the next level, won't be there.
In order to get to one of these, first go to the main entrance to the garage. Open the map and chose any barn you want. When you get there, you'll find yourself in a location containing one or more vintage car. You should also look through all boxes and shelves - you may find some interesting parts there. However, think well if you really want to take the given part: not all of them can be repaired, and some of them are not in a condition that would allow fixing them into a car. Besides, you have to pay for everything you take from a barn.
Remember: if you but leave the barn and immediately come back, all items stored there before exiting will be irreversibly lost. So, without some serious cash, there's no point going to barns (the average price of a car from a barn is around 20 000$ or not much less).