My wife has a WordPress blog and over time everything has been slowing down until the site pretty much stopped working all together.
Optimizing WordPress is a very large topic with many resources online. Following a couple different web site suggestions, I decided to start with the plugins as these are known to cause issues. My wife had about 30 installed. After deactivating all the plugins, things started working much better. I installed some plugins to assist with determining the plugin(s) causing the trouble.
After enabling plugins one-at-a-time and profiling the page loading using P3, I discovered that JetPack was causing the blog to have some major slow down. Little did I know, but many modules in JetPack were enabled by default and weren't being used. In fact, page load time went from 0.10 seconds to 1.5 seconds per page.
Disable Unused JetPack Modules (or JetPack)
If you click "Learn More" you will then see a new button called Deactivate. This button will turn off this module and will help to make your blog faster. I strongly suggest choosing to deactivate only the bare minimum to reduce unnecessary resource usage. If you can, do not use the JetPack plugin. Once the developers are able to increase their code performance, it will be worth looking at again.