You get T-spins in any mode of the game. Just choose an easy mode with a slow speed.
What you need to do for a T-spin is place a T-shaped piece into a T-shaped slot by spinning
(rotationg) it into place. I mean there is a horizontal T-shaped slot that you can't get to normally, so you wait for the T-shaped piece to fall vertically and then at the last moment you rotate it which will place it in the slot.
To be sure you've done a successful a T-spin, watch out for a T-spin icon that appears on the lower left of the screen as soon as you've done one.
I found this good tutorial on how to do t-spins here:
(not my video, it's a different Tetris game but it works all the same)
Once you get the idea of what a T-spin is and how to get it, you can get it fairly quickly. I was done in like 10 minutes.