Assuming your search field is an outlet in the nib file and is called "mySearchBar"
Code:
NSString *searchURL = [NSString stringWithFormat:@"http://www.google.com/search?q=%@", [mySearchBar stringValue]];
Then you just load that URL in your web view.
Code:
[[myWebView mainFrame] loadRequest:[NSURLRequest requestWithURL:[NSURL URLWithString: searchURL]]];
This is a simple example, you can probably work from here