It's a very good tool, but the advice given won't always improve your speed. Most of what it recommends are things that are good standard practices you should consider, but they won't improve every website.
So I wouldn't worry too much. Those tweaks won't always speed things up overall. Still some very good things to follow if you aren't experienced in site optimization though.
Without re-coding your website/script/app, some of the easiest ways you can reduce the load time of your website are:
1. PHP op-code caching (e.g., APC, XCache, etc).
2. Image sprites.
4. Reference your static images using multiple subdomains. Web browsers limited the maximum number of concurrent requests on a single hostname. You can 'trick' the browser to making more requests at once by introducing multiple subdomains.
5. If your server doesn't have a high CPU or IO load, add GZip compression.
6. Use mod_expires to leverage browser caching.
If you haven't implemented those measures, you'll definitely realize significant performance gains with them.
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I agree with @koolkeys. You often don't get drastic improvements, even if the score gets slightly better. I'm using the tools to spot problems when the site seems slow, or monitoring tools report some kind of issue.
Google page speed and Y Slow (by Yahoo!) are two of the best tolls available to optimize page load time. Since Google considers page load time as one of the signals for SERP, you should also try minify and CDN.
Are you using a CMS? Outside of the general speed improvements you should search online for tip and tricks to speed up the CMS you are using. I use Concrete a fair bit and I've found some very useful tips online which improved the speed vastly.