C Documentation for AVR Atmel Studio
Atmel Studio 6 provides the Atmel Software Framework which is a massive, if bloated, set of libraries for all the various hardware configurations that Atmel offers. Atmel has done a pretty good job of using doxygen in these libraries so you can find a pretty thorough set of documentation here. 

The ASF is fairly well integrated into the IDE with some C example projects which should work out of the box (assuming you are using a dev kit or otherwise supported hardware).

The avr-Libc documentation is also a great source of information about this particular flavor of C. The rest is mostly gcc C syntax. 

Lastly, while EE.SE is a great site, for AVR specific things you also might want to try asking a question over at AVR Freaks. I think the ASF documentation is relatively self-explanatory, but for things like project setup and tool-chain problems, that site is probably your best bet.