A sticky joystick can ruin your gaming experience; the sticking makes the controller harder to use. If you're dealing with an older controller that's beginning to stick, the problem is likely built up grime and dirt. Clean the external parts of the joystick with rubbing alcohol. If this doesn't loosen it up, you'll need to disassemble the controller to clean the inside and ensure that the joysticks are seated properly. Note that opening your controller voids your warranty.
Clean the Outside of the Controller
Set your rubbing alcohol, cotton swaps, clean cloths and any other supplies out on a flat surface, such as your kitchen table. Ensure that you have ample room to work.
Dip your clean cloth in a small amount of rubbing alcohol and wipe at any surface grime on and around the joystick. Depending on how dirty your controller is, you may need to do this several times to get it completely clean.
Dampen a cotton swab with rubbing alcohol and clean around the bottom swell of the joystick where it dips into the controller. Move the joystick around to ensure you get all possible angles. Clean around the circular edge where the joystick fits into the controller to check that there isn't gunk there tightening up the works.
Disassemble the Controller to Clean Inside
Acquire the right screwdriver for taking apart your controller. If you're disassembling a PlayStation 3 (DualShock) controller, you'll need a small Phillips screwdriver. If you're disassembling an Xbox 360 controller, you will need the less standard Torx 8 Security screwdriver.
Remove all the screws from the body of your controller. If relevant, remove the battery pack from the Xbox 360 controller. The PS3 has five screws on the back of the controller. The Xbox 360 has eight in the back, with one hidden behind the bar code sticker. Set the screws aside in a safe location.
Take your controllers apart carefully; set the controller face-down and pull the back straight up. Both the Xbox 360 and the PS3 have internal components that aren't glued in; these pieces can fall out if you jostle the controller wrong. While everything can be reassembled, it complicates the process.
Clean the joysticks inside the controller with cotton swabs and rubbing alcohol. You may need to remove them from the circuit board, if they're very dirty or sticky. You can take this time to clean any other internal components that may need the attention.
Check that the joysticks are seated properly on the logic board; move them around a bit after they're clean to see if the function has improved.
Screw the controller body back together when you're done cleaning and reassembling your controller. Reassembly will be the opposite of what you did to open the controller.
You can use rubbing alcohol wipes in place of clean cloths.
For new controllers, it may simply take a few days of use to loosen up the unused joysticks. If they don't loosen up after use, consider contacting the manufacturer.
Don't use too much rubbing alcohol when saturating a cloth or cotton swab. While rubbing alcohol evaporates quickly, it is still a liquid and getting too much into your controller may cause damage to the components.