Plastic squeaks when two surfaces rub against each other and cause friction. To prevent the squeak, prevent the friction. The simplest way to do this is to insert another, non-squeaky substance into the place where the plastic meets whatever is rubbing on it. Depending on the location of the joint, how easy it is to access and how often people need to touch it, block the contact using either a basic lubricant or a strip of felt tape.
Identify the two surfaces contacting and causing the squeaking. Check how much space there is between them and consider how often people need to touch the area. Determine whether you can remove one surface temporarily to repair the problem.
Remove one surface if possible. If there is space between the two surfaces when both are in place, apply a strip of felt tape to one surface so the two surfaces will not come into direct contact.
Rub a white, unscented votive candle against the place the surfaces connect if there is not enough room for felt tape. The paraffin wax acts as a lubricant and helps surfaces slide against one another.
Spray a household dry lubricant spray against the area if people handle it often. Hands will rub off paraffin wax, but the lubricant spray has greater sticking power. Also use dry lubricant spray on joints where you cannot remove a surface to access the joint easily.
Replace the surface you removed. Check the plastic for squeaking. If it continues to squeak, remove the surface again and add more lubricant.