Building a website in 2012?

If you are planning on developing a new website, here as some concepts (some old, some new) on how to go at it:

Think responsively – Even if you’re not implementing a full responsive design, simply thinking in responsive terms goes a long way to achieving usable universal design.
Think touch-first – A button sized for a fingertip will always work for a mouse cursor. But a button sized for a mouse cursor will often be too small for a fingertip. Designing for touch first ensures that your website or application translates well to other contexts.
Think universally – "Test early, test often” the saying goes. In your design process, think early and often about how your design will function on various devices.
Think mobile-first – Starting your design with mobile focuses you on what really matters to your users. By maintaining focus on the essential features, achieving a consistent experience across devices will be much easier.
Be careful with interaction behavior that is not supported universally across interfaces. Hover states don’t function the same on touch devices. Touch gestures can’t be performed with a mouse. It doesn’t mean we can’t use these things, but we have to be aware of their limitations.
Full article: Designing The Well-Tempered Web by Rob Flaherty at Smashing Magazine

See also an excellent directory of responsive-designed sites.