Okay, I said I'd return with examples of non-profs who have received these grants, tracking the performance of your AdWords advert, and applying for a Google grant. Let's dive in...
A first example of a recipient of a Google grant is Room To Read, who "partner with local communities throughout the developing world to provide quality educational opportunities by establishing libraries, creating local language children's literature, constructing schools, providing education to girls and establishing computer labs." As listed on Google's site, just one click thru from one of their AdWords impressions brought in a donor who donated enough monies to support the education of 25 girls for the next 10 years. That's a pretty impressive result from just one click thru.
Another example is coachart, dedicated to improving "the quality of life for underprivileged children and adolescents with chronic and life-threatening illnesses by providing free, personal lessons in the arts and athletics." Google reports a 60-70% increase in volunteers since the inception of the program for coachart.
Tracking the performance of your AdWords isnt too difficult. You're provided an administrative access to your dashboard containing 1) clearly defined labels for which key words you placed, 2) the status (active or inactive), 3) clicks and impressions, 4) and a variety of statistics regarding costs and conversions. I've cut-and-pasted below the image provided by Google on their site. Comprehending the value of the stats that they provide may present the greatest learning curve when using the dashboard - I'd recommend bringing in your development team to estimate value, searching Google's content online for an "about" on this, or contacting Google directly. I use their Google Analytics dashboard (different from this one) for my personal blog and its a great help, but I do NOT comprehend all the stats they provide (and it is robust.)
Finally, for as for how to apply, as a default I'll say, first be aware that Google's philosophy for the grant is to assist organizations that share their "philosophy of community service...with a strong mission to help the world in areas such as science and technology, education, global public health, the environment, youth advocacy, and the arts." If you fit in the realm, which I'm certain you would, look first to their "availability and eligibility". After reading that information, you can fill out the APPLICATION. Beware - they'll request information such as 1) what is an example of an ad you'd run, 2) your EID, 3) some web statistics from your current site, 4) keywords, 5) affiliations, et cetera.
That's the down-n-dirty, enough to get started. Hit me up if you have further questions. Best...James