input: [1] Google [2] url IP search terms date/time city/state/country (from IP) identity (possibly) [3] They record the URLs you visit to improve their search results, and also to provide you with features. If you have a gmail account, a Google account, a YouTube account, etc. and you have cookies enabled, Google knows specifically who you are with every search you do and can do things like show you (optionally) your search history. [4] They say they keep data at least 9 months. (Presumably they keep the data indefinitely if they have your permission as part of a feature of theirs, or if they dis-associate it from your IP.) [0] 
output: Google receives and responds to the request, via the ISP.