GoKawiilYour first port of call should be to give your DualSense a good clean. Dust, grime and the sweat from your fingers can all negatively impact your controller's sensors. As for how you should clean your pad's sticks, your best options are either to use a can of compressed air or a cue tip/cotton bud lightly dipped in rubbing alcohol. With the former method, ensure you only use short, intermittent sprays; as for the latter, please don't overdue it with the alcohol. Whatever method you go for, turn your DualSense off before you attempt to clean it.
Resetting a PS5 controller can also help eliminate stick drift. After you switch off your DualSense, turn it over and locate the small reset pinhole on its rear. Once you've found it, use a paperclip to gently press down on this button for at least five seconds. You can then pair the pad with your PS5 using a USB cable.
Though stick drift is mostly caused by hardware problems, software issues can also wreak havoc with your gamepad's inputs. If the above cleaning or reset methods fail to work, try updating your controller's firmware. You can do this by going to Settings > Accessories > Controller (General) > DualSense Wireless Controller Device Software.
For those of you who own Sony's ultra-expensive DualSense Edge, you have an additional option to banish stick drift (though sadly it's not free). If none of the methods above work for you, you can buy a new DualSense Edge Stick Module for $30. Though it's annoying Sony doesn't ship its $200 pad with replacement modules, at least they're easy to swap in.
First up, slide the release latch on the back of the controller to the left, then pull off the plate surrounding the sticks. Each stick has a metallic release latch that can be pulled up to allow you to slide a faulty stick out. Once you yank the stick out, you can simply insert the new one, before securing it in place by lowering the release latch. Pop the plate back on and your new stick will be good to go.