After you have logged into TrainStation through the website (also called the portal) or via app (mobile or tablet version), you will find the minigame under gem shop section (see first image). Pressing the "Start" button begins the randomization process. For a few seconds, a train will pass across the game window, eventually stopping and displaying a wagon with the logo of the resource you have just won. If you want to play second/third time, you must watch the Ads Reward, in order it will then allow you play the second/third time and you would expect as first go progress with final reward displayed.
The amount of the resource you've won will depend on two factors. You get a base quantity that is 50 times your current level (e.g. Level 177 X 50 will yield 8,850 resource units). The second factor will be how many consecutive days you've played. You get a bonus multiplier of Days Played * 10%, up to a maximum bonus of 50%. So if you have played 5 days in a row you will get a 50% bonus (8,850 * 0.5 = 4,425). This means you would receive 13,275 (8,850 + 4,425) resource units for this spin.
Note: Special Spin feature is only available via Mobile platform.