Where do I find the client id and client secret of an existing connected app?

Just navigate Name > Setup > Create > apps and then click on the app you need. The page you load will contain those information under API (Enable OAuth Settings).

In the Enterprise edition I am using, to find the client id and secret for an existing app, I had to go to Setup > App Manager > Down Arrow next to app name > View > look under 'API (Enable OAuth Settings)'.

This was very confusing as you'd think you could go to Setup > Connected Apps > then click on the App name to see it... but nope, it wasn't there. Nor was it there when editing the App. Only through the process above could I find it.