There are a number of things for which every man wishes to have the right words: when you meet the perfect girl, when you're telling your mother about her, or just what to say to the traffic cop when he stops you. This passage assures us of right words. But it seems to prohibit us from preparing for the occasion.
Why would we need to know what to say?
Because we are going to be persecuted for our faith. The state regards itself as supreme; those who think otherwise are a threat. The religions of this world know that you should be more tolerant; no one could possibly be absolutely right—right?
So don't worry about it.
Don't worry about what? Don't worry about how to defend yourself. Why not? So that you will say what the Spirit wants said, not what you want said.
Don't worry about what? Don't worry about the words you will use. Why not? So that you will not be tempted to sit up the night before in jail, thinking, and thus be tempted to hypocrisy.
The Holy Spirit
If I'm not going to plan what to say, it's good to know that someone is! It's a great reassurance to know that the Holy Spirit has this one covered. But there is another reason: this assures that the honor and glory will belong to God, not to us.
Note that verb. This is not expected to be some form of zombie speech—mouth moving but brain disconnected. We are going to be in this up to the neck. It's just that the inspiration comes from God. They'll know that it's our voice, our passion—and his Spirit.
"At that time"
For those who are perpetually late, this will sound like a blessing. For those who like to plan ahead, we have to wonder why we won't get the words before the trial. But did not our Lord say that sufficient to the day is the evil thereof? Hence we need not borrow any trouble; it will arrive of its own accord, soon enough.
Your author has met the perfect girl, and he didn't know what to say to her. When I took her home to mom, she did all the talking (and still does, the two enjoy each other very much). I've given up on clever excuses to give the traffic cop. Praise God; the defense of the faith does not rest on my tongue, but His Spirit.