Isn't this what Incognito Mode and proxies are for?
Incognito Mode is about not storing information on your own computer about which websites you visit. The NSA has probably deals with most free proxy providers to access the relevant data so that won't protect you. Using Tor does provide some layer of protection but it makes it really slow to access websites.
Does the surveillance state affect us? It has affected me, and I didn't realize that it was affecting me until recently. I give a few examples of how it has affected me: