For the trucking job you'll be working for National Transfer & Storage Co. You can find their building on the corner of Vespucci Blvd and Popular Street:
If you have not yet been hired to the job you'll see a brown briefcase icon. Once hired, that icon will change to the green trucking symbol as shown above, and this is where you'll go to clock in for the job. Outside of the door on the corner of the building you'll see a yellow question mark. Walking up to this marker & pressing E will allow to you apply for the trucking job. You'll see an "Are you sure?" screen. Press yes to be hired!
The first rank in the trucking career is as a Driver. Once hired, the yellow question mark will change into a green circle marker. You'll use this spot it clock in and out of the job. Like with the hiring marker, press E inside the green circle to clock in to the job.
Once you're clocked in you'll receive a message on-screen letting you know that you've clocked in, and where to find the truck rental. If you own your own commercial vehicle, you can skip the rental step. To complete a mission for the job you'll need to be driving either a Phantom, Phantom3, or Hauler. If you need to rent a vehicle, you'll be driving the Phantom.
To rent a truck, simply travel around the north, street-side of the building until you get to a pair of automatic gates. Walk inside of the gates towards the service doors and you'll see a green truck icon.
Pressing E near the marker will rent a truck. When you're ready to return the rental vehicle, drive the truck just east of where the rental spot is. You'll see some parking spaces, with one space designated by a red bar marker. Press E from inside of the truck to return the vehicle.
Once in an applicable vehicle, press K to receive a mission! Generally, there are 2 stages to every mission. Pickup and delivery. You'll drive to a designated destination to pick up a trailer, and then deliver that trailer to the specified drop-off. GPS routes will guide you through both stages of the mission. Don't be afraid to make stops along the way! You'll keep your mission even if you leave your truck, and you can set personal GPS routes if you need to head somewhere else before you complete the task.
For the Pickup stage, simply follow your GPS to the designated spot on the map. When you're near the trailer you've been assigned to pickup, you'll receive a message to attach the shipment trailer to your truck and deliver it. Simply back your truck up towards the trailer. It will automatically slide on and hitch to your truck once you're close enough.
By the time you've got your trailer attached, your map GPS will have already updated for stage 2: delivery. Drive to the new destination with your trailer in tow. Be careful not to damage your shipment! You'll suffer payment penalties if the trailer is badly damaged when you deliver it. And if you totally destroy the trailer, you'll fail the mission altogether.
When you're near the delivery zone, you'll once again receive a message on-screen to deliver the shipment. You should look for 4 identical arrow markers in a rectangular zone.
This is how the customer would like you to park the shipment. Of course, if you're ready to just move on to the next job, you can just park the trailer however you'd like inside of the zone and move on. However, doing a good job and parking as closely as you can within the 4-corner-markers will net you bonus pay!
When you're parked and ready to deliver, press H to detach the trailer and complete the job. You'll receive an on-screen message letting you know whether you did a good job...or whether you didn't. After that, if you're looking to make some more money, simply press K again to receive a new mission!