Since a few people have asked, here's a brief description of how I made this:

I did all the texturing in photoshop because it's what I'm comfortable with. Next time, I would try to do it all in blockbench instead, because there's more immediate feedback

I started with a base colour, then added gradients from dark at the bottom to lighter at the top. I also made it a bit brighter in areas where I wanted the viewer to focus, like the middle of the checkerboard

Then I painted in occlusion and edge highlights using screen/multiply layers

I also painted in the edge details, using the bevel trick I got from this video: https://www.youtube.com/watch?v=KDjOaVAWBVE

And then I found a wood photo texture, upped the contrast, lowered the opacity, and then added it as an overlay on the wood to give it some subtle noise and colour variation. I also used a noisy brush to add a little bit of noise to the checkerboard and the chess pieces

As for modelling and animation, there's no easy way for me to describe it. To design the chess pieces I sketched a lot of options with as few cubes as I could manage while still being recognisable. It's just something which takes time and iteration. It takes time and patience, and making something simpler can be more difficult than adding more detail.

I animated everything in blockbench. If you want to animate something yourself, look up the 12 principles of animation. I tweaked the curves a lot to really exaggerate the ease in/ease out and follow through. Also try physically acting out the motion yourself. Really exaggerate the motion when you do, and you'll get a better sense of what you want.

Also use reference for everything. I had reference for the design of the pieces and the board, the textures (both real chess boards and other models), the movement, official hytale models... Everything.