I did this trip in March.
You must book your trip with Amtrak. You will receive tickets for the train and seperate tickets for the shuttle.
When booking your return trip, the shuttle leaves Laughlin at 12:01 AM. I made a mistake on my reservation and booked the wrong day.
When you get off the train in Kingman, the shuttle, (which is a white passenger van with a small box trailer behind it), is in front of the station in the parking lot. And it is waiting for you, so grab your bags from the train and go. They did have a list of people getting on the shuttle and checked it when they took tickets. It goes straight to Laughlin and drops you off at the valet at the Tropicana Express.
Be sure and use the restroom before getting off in Kingman, the shuttle does not stop.
I would take a sweater, the coach cars on the train can be cold.
On your return trip, the shuttle picks you up at the same place, valet, Tropicana Express. The shuttles website, states to be at the Tropicana Express 45 minutes early. We were there one hour early, the shuttle came at the time of departure but I would definitely be there early. The shuttle drops you off at the Kingman station and there is not much of a wait for the train if it is on time.
I did not talk to the shuttle driver about my return trip, I had my tickets so I knew they would be there.
While waiting at the Tropicana Express to come home, there are slot machines and restrooms by the door out to the valet.
The shuttle does have a website, CommuterServices.net, there is a page on the Amtrak Thruway with info for passengers.
Have a great trip!