The exorcism ritual stipulates that there are three signs that the priest has to look for: abnormal strength, the ability to understand unknown languages and the knowledge of hidden things. But they're very arbitrary, even those things. So they have to be in concert with something else. And typically what priests look for is what they call the aversion to the sacred, which is a person's inability to pray, to say the name of Jesus or Mary, to even look at the priest. Typically, when the person comes to see them, it's the last thing they want to do. They tend to have gone to see many doctors in search of a medical cure for whatever is afflicting them. They don't believe that the problem is demonic. They don't come in and say, "Father, I'm being attacked by demons. You need to pray over me." When someone says that to them, the priests immediately discounts that the problem is demonic.
Read an excerpt of Matt Baglio's The Rite: The Making of a Modern Excorcist