So you may wonder what a verse in which Paul is accused of being a few leaves short of a laurel wreath has to do with the idea of joy.
Well, we'll look first at the sermon that John Wesley preached from this verse and I'll see if I can't connect the dots. Wesley was often accused by his detractors of fomenting "enthusiasm" among those who listened to his preaching, which did not mean the same thing it does for us today. After all, we can probably point to a number of church folks who would never be accused of enthusiasm and a number of preachers who wouldn't dream of fomenting it.
But in church use in the 18th century, "enthusiasm" referred to overt responses and displays during a worship service. Sometimes it might be one of the spiritual gifts described in the New Testament, like speaking in tongues. Sometimes it might be breaking down in tears or displays of great happiness, or some other demonstrative act. The common thread was that proper people didn't act like that in church. It was poor behavior. Well-bred, well-brought-up people knew better.
Wesley rejected the idea that "enthusiasm" had no place in worship. Obviously, there were and are standards of behavior in worship that avoid rudeness to fellow worshipers and display courtesy to them and the speaker. But if the Holy Spirit was at work, then those standards took second place. After all, he often preached to people that the proper preachers didn't bother with, since he was speaking in fields, village squares and hillsides. Many of them may not have ever heard the gospel before, and learning that God loved them in spite of the fact that they were not well-to-do or the "right kind of people" could bring a powerful response. What his critics called "enthusiasm" Wesley called proof of the Holy Spirit at work in the people listening to him preach.
When Paul testified before Festus, he not only explained how he was innocent of the charges against him, he also talked about Jesus and what he had done. In other words, he testified in both the legal and church senses of the word. He did so as a response to what God had done for him, and Wesley said that his listeners did what they did in the same way.
And "joy" is the same kind of thing. We often confuse it with happiness, but they are not the same. Happiness often depends on external circumstances. We know that we might feel happy now, but something could happen that makes us unhappy soon enough. Maybe we get tired. Maybe someone cuts us off on the road, or brings 40 items to the 20 items or less line. Or maybe something serious happens. We know that happiness doesn't always have staying power.
But joy as God gives it is different. It's like Paul's testimony or like Wesley's enthusiastic listeners -- a response to something God has done, rather than a feeling that depends on what goes on around us. Joy may come in the middle of great things, certainly. But sometimes it comes in the middle of hard times. When Paul wrote his letter to the Philippians, which is pretty much dunked in joy, he was in jail and awaiting word about whether or not he would win a legal appeal that would save his life. He wrote about joy not knowing whether he was living his last day.
And joy can come in perfectly ordinary circumstances as well. If you saw the video of US Air Force Orchestra musicians doing a "flash mob" concert at the Air and Space Museum you can get a picture of that: People are just going about their business at the museum when all of a sudden musical instruments appear and begin Bach's "Jesu, Joy of Man's Desiring."
In that sense, I guess Festus was right. We Christians may have lost our minds, because situations that might provoke despair or boredom or even nothing at all often seem to bring us none of these things. Instead, we respond with joy. The trade seems like a good one to me.