As cliched as it is: The greater your experience, the more you know how little you know.
OT: Interestingly I just came across my first 'expert sex change .com' link in years a few days ago.. for some ugly and stupid legacy server error, naturally I swore at the site again, and told my colleagues about how much we 'hated on that' in the day.
For more general questions not covered in the doc I Google about twice to 4 times a day in average. I usually go to stackoverflow.com directly to search.
When coding HTML/CSS/Javascript I clearly lookup caniuse.com about 20 times a day to ensure consistent browser support and learn about corner cases.
suppress STDOUT print ruby backticks
mechanize user agent alias list
git gc garbage collect source
There is no shame in googling. While I would heavily recommend reading and learning documentation, once you get a passing familiarity (not memorize it) you at least understand what you are using and googling it simply can save time. If you need specifics on the implementation the docs will always be there.There is a reason we have SO and google is so great at finding things on it. Have no shame :) It doesn't make you a poor programmer to be thinking things out enough you are googling alternatives, how the innards of something works, etc.
Obviously this is all just my opinion, though. I could be a moron and not know it.
And these days, the docs are usually online, and usually don't have a great dedicated search engine, so often googling is the best way to find what you are looking for in the docs, anyway.
For a language like Java, I mostly google to see if what I want to do already exists in an Apache library or is now part of the latest JRE. For well-documented Java frameworks which have JavaDocs attached, googling isn't often necessary.
Nine times out of ten I end up at either Stack Exchange or W3Schools.