There are a few things that can cause iMessage to turn green, and none of them are particularly pleasant. Let's take a look at what might be causing this problem, and how you can fix it.
The first possibility is that your iPhone is out of battery power. When this happens, iMessage will automatically switch to SMS messaging, which uses a different protocol and doesn't allow for the same features (like read receipts) as iMessage. This can be frustrating, but fortunately there's an easy fix - just charge up your phone!
Another possibility is that your iPhone is in Airplane Mode. This mode disables all wireless radios on your device, including cellular data and Wi-Fi. As a result, iMessage won't be able to connect to the internet and will again fall back to SMS. The solution here is also simple - just turn off Airplane Mode and re-enable cellular data or Wi-Fi (whichever you were using before).
If neither of these solutions work, then it's possible that there's an issue with your carrier's network. In this case, you'll need to contact your carrier directly for help troubleshooting the problem.