My first step would be to learn both the display: flex and display: grid syntaxes. They eliminate the need of 90% of the hacks of floats/clearfixes, and table layouts. For this you can get familiar with the overall possibilities with these games: - http://flexboxfroggy.com/ - http://www.flexboxdefense.com/ - http://cssgridgarden.com/

The next big bite to take is responsive web design, using Media Queries, which involves getting mostly rid of any fixed width and rely on %, calc() and modern units like vw and vh to size your content.

CSS Tricks has a great article to get started: https://css-tricks.com/css-media-queries/

Good luck to you on this new adventure!