Car Auctions are automatically unlocked once you reach Level 15. To access the Car Auctions you will need to press Triangle to open the quick menu and then select the Map. Once the Map is open, you will see Car Auctions and you can travel to it. Once the loading screen finishes, you will have 2 options to choose from, Kowalski Car Auctions and Kowalski Salvage Cars. Both options will allow you to buy cars that will count towards this trophy. However, Kowalski Salvage Cars tends to have cheaper cars, so if you are going specifically for this trophy, it might be a better choice.
When picking an Auction, you will have a list of cars available to choose from. Pick the car you want and you will be transported to where it physically is so you can inspect it if you want. To buy the car, right click when looking at it and and pick top option start the Auction.
The actual bidding screen has a lot of information and may be confusing at first but the only thing you need to focus on is the large circle, which will deplete with either a Green circle if you are the highest bidder or a Red circle if someone else has the highest bid. All you need to do is keep spamming Space to remain the highest bidder BEFORE the circle timer depletes or you will lose the Auction. Eventually, you will be the highest bidder and you will win the car and can then choose to send it to your Garage or to Parking.