The first thing that you need to be aware of is that there are many different ways to remove the data from your hard drive or to otherwise render it unreadable, but for the most part, you will find that this involves destroying the discs and plates that hold the information that you have put on there. These discs or plates can be destroyed or you will find that they need to be overwritten, that is, that the information that you have put on needs to be overlaid with other information. In any case, you will find that a very thorough, very exacting job needs to be done before you can be sure that the data has been destroyed.
One way that you can dispose of your hard drive is physically. There are services that will grind up the hard drive physically for you and you will find that because this involves the physical destruction of the plates and discs that your data will be disposed of. Keep in mind, though, that even though this is something that you can take on, on your own, that it needs to be fairly precise. Even driving over your hard drive will not necessarily destroy the information! Many of the pay services that you can go to for this particular kind of hard drive disposal will actually cut the hard drive into strips before grinding it down to crumbs!
The other method that is used to destroy hard drives before they can be safely disposed of is magnets. Essentially, you will use magnets to destroy your data in a degaussing process. To do this, you will find that you are going to be using powerful magnets and laying them out on a clean surface. You will pass your hard drive over them several times, alternating the exposure of the magnets. While this is effective, you will find that it can be tricky to make sure that you get everything.
When you are looking at methods to get your hard drives ready for disposal, don't forget that there are professionals out there who will help you do just that. This can go a long way towards easing your peace of mind and giving you the security that you need.