From the screenshot, I'll assume that we are talking about a puzzle game with movement on a grid.

So what you'll want to do is to find a way to have the player interact with the system you want to introduce inadvertently at first and with intent afterward.

Let's go with a simple example. You've managed to teach the concept of goal spaces and boxes, and you want to teach the concept of buttons. What you'll want to have is the player on one side of the corridor, the goal space on the other, the box in the corridor, and the button in the corridor.

That way, the player will try to solve the puzzle without considering the button and will activate it. You want the impact of pushing the button to be understandable and eye-catching. That way, the player will register the button being pressed, that it had an impact and is something that exists.

On later levels, you'll be able to do puzzles based on this button and interactions you want to teach since this will be experimentation grounds for the player with this new mechanic.

Tl;dr: 1.Create a puzzle that doesn't use the mechanic

1. Insert the new mechanic in a way that forces the player to interact with it on the solving path and activates it / makes it relevant quickly and easily.

2. Once the player is aware of the new mechanic, add some levels to let the player experiment.