Corona SDK is a separate product from Xcode. Corona SDK uses Xcode’s utilities to build your app, but the Xcode doesn’t know or need to know about Corona.
To upgrade Corona, simply download the latest version (public of daily build). Double click on the file that downloaded. Since you’re asking about Xcode, I’m assuming you’re on a Mac. This file will be a .dmg file. It will open a window and you simply drag the Corona Icon to the Applications Folder Icon. If you’re using public builds, it will write over the previous version. If you’re using daily builds it will create a new application in /Applications named after the build number, for instance CoronaSDK.2934. That way you can test different daily builds with out overwriting the public build. Then simply run the Corona Simulator from either the public build folder (if that’s what you updated) or from the new folder of the daily build.
Corona generally requires you to also keep your Xcode up to date. When you go to build in Corona (CMD-B) the dialog box will list an iOS SDK. Mine currently lists 9.3. We do change this from time to time as Apple issues new versions. Your Xcode should match this version, but it’s two numbers behind. For instance if you’re using a Corona SDK that is using iOS 9.3, you need Xcode 7.3 installed.
Later today, I expect Apple to release iOS 10 to the world along with Xcode 8. When we turn on iOS 10 as an option, if you want to use that you would need to install Xcode 8 first.
Rob