There are quite a few tools which can help measure website performance from ping plotter (desktop freeware) or just search online for "website performance tools" e.g. tools.pingdom.com, webpagetest.org, gtmetrix.com etc. The important thing with testing is to examine how your website performs in different locations e.g. US, Canada, Europe etc.
To be blunt I'm not too bothered about Google getting rid of this tool.. For the most part I have noted that the recommended changes can be difficult to implement, especially when using CMS's such as Wordpress.
For me I keep it simple. My focus is on:
1) Good performing reliable host.
2) Ensure images are scaled accordingly.
3) Minimize the number of plugins. If you can avoid using a plugin in favour of using alternative approach then go for that e.g. embed script/code to header/footer, use htaccess etc where possible.
At the end of the day if my website loads within a couple of seconds then I'm okay about it... Most users would be okay with that too... and hence I personally do not bother to spend time/efforts on improving on that when we are talking about Milli-seconds etc.. It seems to me that Google's page speed tool seems to always spell out doom regardless, even when you are happy with the current performance.. Perhaps that's part of the reason they are getting rid of it lol...
Overall I would say keep it simple... Test your website at different geo locations and ensure the main areas are optimized for performance e.g. images, plugin/scripts, web hosting etc...