The bottom part of all chess pieces is very similar. One might say identical. Let's draw the bottom part separately. It looks like a layered cake made of different pancakes.
Now, using this base, we'll draw each of the pieces.
The simplest is the pawn. It has a concave stem with a ball on top.
The bishop isn't much more complex. Basically like a pawn, but with a spike on top instead of a ball.
Next in complexity is the king. It's large. It has a cross on top of its ball.
The queen is slightly more complex. The wavy edges of the crown are quite intricate.
The rook looks simple and angular, but drawing the tower is difficult, especially in three dimensions.
And the most challenging (if you, like me, can't draw horses) is the knight. I'll remind you, a horse without a mane looks like a dinosaur. So draw a dinosaur and add a mane to it.
And there we have our chess set.