While the keyboard navigation and other Google Instant enhancements have not made the mouse or trackpad totally obsolete for doing Google searches, they have made searching and displaying search results much less tedious affairs.
Here's how I use Google Instant with keyboard shortcuts in the Safari web browser on my Mac.
While typing what you want to search for in the search box, Google will suggest terms that are related to the keywords you're currently searching for.
In the following example, I'm searching "movies for kids". After I'd typed "movies for", Google suggests "kids" (displayed in light gray), which is exactly the next word I'm looking for.
To go ahead with the suggested "kids" and autocomplete the search query phrase, I can press Tab or Right Arrow on the keyboard. I prefer Right Arrow.
There's also other suggestions that come up in a list directly under the search box. I can select any of those by hitting Up Arrow or Down Arrow on my keyboard.
Google Instant will immediately display search results for the terms you've actually typed in, or for the search phrase that is a combination of whatever you've entered so far and any suggested term in light gray. Also, the search results will dynamically change every time you select a different query from the search suggestions list. Do note that there's no need to press Enter for this to happen
When you're comfortable with the search results you're seeing, press Enter. You will see a tiny arrow pointer next to the first search result.
You can navigate the search results by moving the pointer with Up Arrow and Down Arrow on your keyboard.
A pointer at a search result means that particular result is currently selected. To get an idea of what the web page looks like for that result, press Right Arrow. This brings up Instant Preview to the right of the search result.
Instant Preview continues to remain open while you press Up Arrow or Down Arrow. This lets you see what the web page for the previous or next search result looks like.
To hide Instant Preview, press Escape or Left Arrow. I prefer Left Arrow.
To open a web page for the currently-selected result, with or without Instant Preview visible, press Enter to open the web page in the current browser window. Press command+Enter (Ctrl+Enter in Windows) to open the web page in a new browser tab. I always open a result in a new browser tab whenever there are multiple web pages I want to take a closer look at.
When you're at the last search result (there can only be ten results per page), hitting the Down Arrow one more time places the pointer at Next. To go to the next page of results, press Enter (command+Enter, or Ctrl+Enter in Windows, to open the next page of results in a new browser tab).
To change your search query or enter a new one, just press any other key on your keyboard (there are a few you can't use such as the Spacebar, comma (') and quote (") keys). Doing this immediately puts your cursor in the search box, adds a space and the character you just typed after that. Alternatively, you can hit delete (Backspace in Windows) to immediately delete the last character from the query.