The cart is basically a car. In order to drive a cart you have to complete a quest. The quest can be obtained by anyone level 50 or higher. The cart is owned by the player, and the player can buy better pieces for the car to improve its performance. You can also equip cart weapons. There are some advanced artisan who can make the cart body.
There are different schematics you can get either purchase yourself to learn (from other player, NPCs or Event NPCSs) or recieve as drops. Check out all the categories by visiting Cart Schematics