There was a thread of this, but it was a question, and the answer was quite vague. I decided to make a proper tutorial of it here.
The elevator was originally suppose to work by itself, but there was a mistake with the elevator starting.

1. Create the elevator in your map. Make a func_instance and set the VMF filename to Instances/underground/test_dome_entrance_lift_01.vmf.

2. Select the elevator, and you will see an "Edit Instance" button. Click on this, and it will take you to the vmf of the elevator.

3. Create a logic_auto in the vmf of the elevator. Create the following output:
   OnMapSpawn
   entrance_lift_train
   StartForward
   Delay: 0

4. Save this vmf (or if you want to, save it as another name.)

5. Back to your map, create an info_player_start and place it in the lift of the elevator.

6. Test! Hope this helped anyone who has questions.

Vordwann wrote:
All I did was fix the trigger in there and add the info_player_start, without any logic_autos

Yes, but adding a logic_auto would be the cleanest way. Also, I did the trigger in the elevator, it worked for a while then it just stopped working for no reason... this should work all the time.

UsCobra11 wrote:
I did the trigger in the elevator, it worked for a while then it just stopped working for no reason... [the logic_auto] should work all the time.

You're right, use a logic_auto.