The game says that I can collect my vehicles from there, but how?
You will need to go to the specific garage you selected the car to be delivered to. If it didn't ask you which garage you wanted then you only have one so go their. Go on the map and look for the garage (use the legend on the right hand side to see the available garages.) When you arrive at that garage you need to simply walk into the blue circle or into the garage door. This will teleport you inside in which you will be able to see all your vehicles.
You can also use your phone to ring a mechanic to deliver your vehicle. This is only available online though.
Be aware that it can take around 5 minutes to deliver the car to the garage. You will receive a message via your in-game phone when this is.
If nothing shows then you may not of even purchased a vehicle, make sure to use the internet feature on your in-game phone, navigate to travel and transport and browse the websites.
Special vehicles such as Tanks will not be delivered to a garage and will require you to call Pegasus to arrange a delivery.