Not a techie but even I've managed it. Unscrew case and remove. Pull ribbon cable out back of hard drive. Undo any screws that hold the hard drive in place (maybe a metal strap). Take out hard drive and smash repeatedly with a hammer. Put case back on computer. Take everything to the dump.
Old PCs don't seem to be wanted by anyone as they move on so quickly. The dump recycles them so the bits end up as something else which is better than just landfill.
If someone wanted to dig the drive out the bottom of the dump's container to spend ages working through a smashed up reformatted disc to find an old letter or web cookie they were welcome to. Nothing naughty or top secret hidden on there.