Why Should I Shred Files?
When you delete a file from your PC, it sends it to an area called the Recycling Bin. Most computer users today are familiar with the concept of the Recycling Bin in Windows; anything in it stays in physical memory until you use one of any number of methods to empty the Recycle Bin. You can right-click on the icon and click on Empty Recycle Bin; you can open the folder for the Bin by double-clicking on it, and then clicking where it says "Empty the Recycle Bin"; you can even go so far as to select your files and press Shift + Delete, skipping the Recycle Bin entirely and permanently deleting files from your hard drive in one step.
But your computer isn't really deleting those files. Instead, references to the "deleted" data are removed from your file system's directory structure, and the space they occupy is marked as available for overwriting. Your computer can then save new data in that available space, but until it does the data could still be retrieved.
There are a number of tools out there that allow users to retrieve files that have been deleted from the Recycle Bin1, and a large number of these tools can be downloaded free of charge. Following are several ways to protect your data from most, or even all, of these tools.
Software File Shredders for Individual Files
Often, you only need permanent deletion of individual files that contain sensitive information, such as digital banking or legal documents. Several tools exist for this purpose, some of which are discussed in The Best Free Secure Delete Tools for Windows. When looking at descriptions of these options, it's always a good idea to make sure that the software will not only delete the files you select, but also wipe the disk space to eliminate stray data. Most file shredder programs will do this by overwriting the deleted files with random binary (0s and 1s) data, corrupting the data until it is nearly, if not completely, impossible to recover2.
Software File Shredders for the Whole Hard Drive
Formatting a hard drive in its entirety erases data in a similar fashion to emptying the Recycle Bin in Windows; that is, it will delete the file system's directory structure entirely, and mark the entire drive as available for overwriting. Data can still be recovered from a hard drive that's been formatted once. The more times a hard drive is formatted, the less likely that data is recoverable. Peter Gutmann designed a method in 1996 which required a user to format a drive seven times for maximum efficacy in ensuring permanent data erasure3. While his method is a little dated, it is still effective and is widely used today.
There are a couple of ways to go about this. The easiest way is to download Darik's Boot And Nuke, which is a boot program you can burn onto a CD and run from the boot menu of your computer. You can also use your chosen operating system's installation discs to wipe your hard drive. Follow the prompts on your screen to delete and create partitions.
Be careful using either of these methods; as the name of this section suggests, your entire hard drive will be wiped out, including your operating system and its files. Be sure you have a copy of your operating system already burned off onto another disc before performing these steps.
Do It Yourself File Shredder for Hard Drive
There is no better way to make your files permanently and completely inaccessible than complete destruction of your hard drive. As you might imagine, this method prevents you from ever being able to use the hard drive again; but if you want to be absolutely certain your sensitive data is unrecoverable, this is the way to go.
Hard drive destruction can take a number of forms. One of the easiest ways to destroy your hard drive is to drill one or more holes through the entire disk, including the platters inside. This ensures the platters that hold your precious data can never spin correctly, and can therefore never be read. Another easy method is to take the casing apart and take sandpaper or another rough surface to the mirrored surfaces of the platters until the shine is gone4.
Of course, your options for total hard drive destruction aren't limited to these. Feel free to use your imagination, be safe, and have fun destroying your hard drive however you choose!
 Fitzpatrick, Jason. "Five Best Free Data Recovery Tools", https://lifehacker.com/5237503/five-best-free-data-recovery-tools
 Miller, Sam. "The Usefulness of the File Shredder", https://www.streetdirectory.com/travel_guide/126348/computers/the_usefulness_of_the_file_shredder.html
 Gutmann, Peter. "Secure Deletion of Data from Magnetic and Solid-State Memory", https://www.cs.auckland.ac.nz/~pgut001/pubs/secure_del.html
Verducci, Anthony. "How to Absolutely, Positively Destroy Your Data: DIY Tech", https://www.popularmechanics.com/technology/how-to/computer-security/4212242