What should an experienced graphic designer working in print learn in order to become a good web designer?

There's two possible ways to start this. Path One, you only design the flat website layouts say in photoshop and hand them off to a programmer to slice up and turn into a website. In this path you will focus on what makes a good User Experience, there's a lot of resources online discussing such topics of layout, verticle spacing, use of white space, use of color etc. Any website that is built should have a clear purpose such as "I want the customers to phone in, email, make an appointment, purchase a product etc" Whatever that KPI is (key performance indicator) you want to design the UI to compliment it.  Example - the customer wants the user to call in - make sure the phone is highly visible with a call to action in the header of every page. Path Two This involves actually taking your design and taking it all the way to completion. You'll need to become experienced in HTML to create the structure of website, followed with CSS to apply the skin over that structure. (the design). These languages will allow you to create basic informational websites. However if you want your website to become functional - as simple as say having a form to submit an email you'll want to study Javascript.  This is a very different method of programming compared to HTML/CSS, but it will be necessary. I recommend http://codecademy.com as the best way to learn coding for free online. There are tons of code snippets, plugins and opensource technologies that you can leverage - however I can't overstate the importance of learning to code by hand.  Stay well well away from visual website editors like dreamweaver.