If you have a RW DVD, there are utilities to erase it, or you can overwrite it with something. Like hard disks, there may still be magnetic traces. If your DVD is +-R, write once, you can't soft erase it.
The best so far is to get a DVD shredder. I opted a while ago for the paper only shredder because the cost didn't justify the number of discs I may have to shred in the future. Also, for paper you need those cross shredder that is a lot harder to put the pieces together. For DVD there's no such fine shredding. As long as you can see a piece of silvery metal, you may be able to recover a large chunk of data or video from it. Are they real in CSI?
I have seen the microwave destruction video, taking only 5 sec. But there is a danger of harming your microwave because of the electric sparks. And there is bad smell. The metallic disc broke down pretty evenly, but the fragments are still large.
Here's what I tried, which didn't work, and don't waste your time. With a small craft drill you can destroy the surface easily using the right sander tip. But it is only skin deep. I don't even think that the plastic layer was penetrated.
I used pure sulfuric acid, which didn't do a thing because of the plastic layer protection.
It dawn on me that I have a plumbing torch. I fired it up outdoors, but surprising the DVD's are very hard to die. The plastic doesn't melt away easily, and it didn't burn. You have to melt the plastic until the inner layers are exposed, then there's a little flame and no more.
Here's the result, before I cut them up and put it in the trash a few pieces per collection day. Now, the superior part, after the torch treatment, the discs are, similar to the surface of the French desert made using the same technique, very crispy. You can crumble the discs into very fine pieces with your fingers, or you can hammer them into powder.