does google know my browsing history by virtue of my phone being linked to my google account? I am completely new to the smartphone world - I have just purchased a Galaxy S4. I want to know if there is any way for me to "log out" of my google account and browse (and generally use the phone) without Google being able to associate my history with my account (which I understand is somehow linked with the phone?).

I am a longtime user of various Google services on my non-mobile devices, but I tend to be fairly careful always to log out of google when I am finished with the particular activity (gmail, calendar, etc) so that everything else I do (whether reading espn or anything else) doesn't become linked to my google account.

I am aware of incognito mode and clearing browsing history and cache - are there additional steps to take?
The title of your question sounds like you're talking about Chrome's "web history" feature. When you browse using Chrome (either on your Android device or on desktop), or from Google Now searches, the pages you visit are logged in your browser history. Chrome syncs your browser history to Google's servers, to let you access your history from any computer where you're logged into the same Google account, and for other Google services such as Google Now.

If you don't want your browser history stored on Google's servers or used in this way, go to the Google Settings app, click Accounts &amp; privacy, and turn off Web History. (As Mr Kutch points out, there's also a web interface.)

If you use some other browser that isn't Chrome, such as Firefox or Opera Mobile, Google has no access to your browsing history.