Intelligence comes in many forms. On the obvious side of things, being able to quickly solve a complex mathematical equation or physics problem is an indicator that someone is probably decently intelligent. That said, there are also plenty of less obvious to get an idea of how smart someone really is. If you hang around enough smart, successful people, you'll start to notice that they usually share certain characteristics like being able to listen and process new information. The great thing is that your brain can be trained to get smarter, so study up and try your best to incorporate the qualities below into your own life.
Also, remember that even the smartest people are still PEOPLE, and even they are fully capable of getting it wrong