You'll need a web development language. The current "hot" one is PHP (however Perl, ASP .NET, ASP, Ruby on Rails are all good languages too), also Javascript and the concepts behind AJAX are important.
Database design/development is a must have. You'll also probably want to learn how to build search-engine-optimized (SEO) websites.
Flash can be good too as well as Silverlight.
To decide, I think you'll want to learn the TYPE of sites you'll want to make (media rich sites generally use FLASH, but you'll still need another language to design the rest of the site). You'll also wanna know the PLATFORMs you want to write for (PHP is on all platforms, as well as FLASH, ASP .NET is basically Windows only).
To round it out you'll want a bit of graphical expertise (if you wanna freelance). It's a crowded field, but good money if you can get good at it.