Resources on Noise Circuits
Noise sources are not very different from AC sources. Most AC sources averaged over time are zero mean, yet we still analyze the circuit similar to DC. The difference is we need to consider the frequency of the signal. Get comfortable analyzing circuits in the frequency domain. Bode plots make things make more sense, since white noise sources have frequency content on every frequency but only on average. 

Explaining how to analyze noise in circuits is too long for one post, but there is a good resource.
A great source to learn how to analyze random sources is 
Noise Reduction Techniques by Henry W. Ott
I've used the tequniques in this book to develop systems that measure nV and uV. 

 
Source: http://www.hottconsultants.com/book.html