On the Digital Ocean blog there's a new post with a "practical overview" of how to effectively scale PHP applications, specifically as it relates to horizontal scaling not vertical.
Shipping a website or application to production has its own challenges, but when it gets the right traction, it’s a great accomplishment. It always feels good to see the visitor numbers going up, doesn’t it? Except, of course, when your traffic increases so much that it crashes your little LAMP stack. [...] But fear not! There are ways to make your PHP application much more reliable and consistent. If the term scalability crossed your mind, you've got the right idea.
The article starts with a brief overview of what scalability is and the main difference between horizontal and vertical scaling (scaling out vs scaling up). They then get into a bit more detail about what horizontal scaling is and how it commonly works in relation to the average PHP application (complete with diagrams). They also talk about some things you can do inside your code to help make things flow a bit more smoothly including decoupling between services and user session/file consistency measures. There's also a bit at the end about load balancing but as that depends a good bit on what technology you're using and the actual load, they just provide an overview and some links to other articles and tutorials with more information.