Start with 2 things. The desired layout, and the HTML. You can keep the layout in your head or on paper if it helps. Code the html , without CSS making it as close as possible. Then add the CSS to make it look perfect.
Then comes JavaScript and jQuery to make pieces jump, hide, move or just to position them better than you could do with CSS.
The site you mentioned uses a very large animated gif as a background image. I watched it for a while trying to figure out where to put my coin.
That’s my opinion. Everybody has one, and some may disagree with me. The way you work should be whatever gives you joy.
JΛ̊KE