What is the correct way to leave Thailand on an ED-visa and return before it expires?

If you're attending a university with a degree program, then you just need to get a re-entry permit and be back before the current stamp expires to apply for the next extension.

If you're here attending an informal school like a language school, or Muay Thai course, you should absolutely not leave. There are MANY reports of people being denied entry when trying to leave then return while on an informal ED stay. This is because you told immigration that you NEEDED to learn SO BADLY inside of Thailand, that you needed a visa to do it. They granted that visa. And now you are leaving Thailand, which shows you don't actually need to be inside to Thailand to learn, or you're not that serious about learning.

If you MUST leave for some reason, get documentation showing why you HAVE to leave, like a funeral, family emergency, or something like that. Have documentation. Also get letters from your school stating that you are in good standing, you have permission to leave for this short period of time (the letter needs to include the dates you will be gone), and that it will not negatively affect your coursework. This letter needs to include direct contact information for the highest school administrator so that immigration can call them. You will also need to purchase a re-entry permit.

Even with all of this, there have been people that have been denied entry even after the immigration officers spoke to the school administrator on the phone.

I would recommend against leaving Thailand.