Not entirely clear what you are trying to do, but a couple of suggestions:
- In Safari, the address bar also serves as the search bar. You can set Google as teh default search engine in Settings (Settings App > Safari > Search Engine)
- You can add a web page short cut to the Home screen (as an icon): Open Safari and go to Google. Tap the send iocon (square with an arrow, just tot he left of the adress bar), select Add to Home Screen.
- Download Googles app from the app store.