I think one of the most critical skills for a web designer to know is version control. 'Web designers', by which I assume you mean front-end development; JavaScript, CSS, and integrating UI elements into presentation layer views.

Working with a development team is different than working by yourself. Working with others means collaborating in some systematic way and version control is at the center of that collaboration.

I'd recommend learning how to use git and subversion to get a feel for decentralized and centralized version control systems and familiarize yourself with popular workflows with each.