Google executives would rather you didn't use "Google" as a verb since doing so threatens their trademark, but as you know, it's very common to hear people say, "I Googled it," to mean they searched for something on Google.
The Merriam-Webster Online Dictionary lists the verb "google" as lowercase, but notes that it is often capitalized. The Oxford English Dictionary draft entry shows the verb "Google" capitalized, but some of the example sentences have it lowercase. In searching for an older, analogous situation, I discovered that Bryan Garner says "xerox" is usually not capitalized when it's used as a verb, but sometimes it is.
There doesn't seem to be an absolute rule, although companies prefer that you capitalize trademarked terms if you insist on using them as verbs. The best advice I can give you is to pick a style and stick with it. As an editor, I respect the preference of companies and trademarks, and capitalize titles, especially Google!
Source: Grammar Girl