I agree with your frustration! The Google Ajax Search shows the typical "don't say anything worthwhile" type of documentation. For example, if you follow the skimpy directions literally, the search results show on the same page as the search box.
Notice this instruction: "5. Place the search box where you want by placing <?php gajaxsearch(); ?> into your theme (most likely your sidebar) or simplify your life and use widget sidebars."
Now a modern developer would give a fuller explanation than that.
Examples of further information:
1) Where do the search results show?
2) Does the person installing the plugin need to create a page for the results?
Notice the arrogant brushoff on the Q&A:
Q. It doesn’t work
A. Read the installation guide. (This assumes that the user hasn't tried to make some sense out of the installation instructions.)
Q. It *still* doesn’t work
A. Open up a thread in the support forums tagged ‘googleajaxsearch’ and ‘dancameron’.
(Which support forums would that be? WordPress support forums, or does the plugin writer have a support forum?)
This will make a lovely example to show new programmers how not to document their code!