We never strip or milk a chest tube without an MD order. And never clamp them, either, unless you're trying to locate an air leak. Keep a pair of hemostats and if you have to clamp, make sure either the hemostats are padded or you provide padding (wash cloths can work).
Keep vaseline gauze at the bedside.
Make sure connections are secure.
Keep the drainage unit BELOW the patient and try to avoid any dependent loops in the tubing.
Observe insertion site and note if any eyelets are visible; could be a sign that the tube has slipped out
Monitor water seal and suction control chambers to make sure they are at the prescribed level. Water also evaporates so make sure to look for that too and add more (sterile) water if necessary.
Look for tidaling, which is normal. Absence of tidaling can indicate a blockage (such as a clamp or kinked tube) or could indicate lung reinflation.
Keep a bottle of sterile water at the bedside just in case.
Observe for bubbling. Intermittent bubbling indicates air is leaving the pleural space which means the pneumothorax is resolving. Continuous, rigorous bubbling indicates an air leak. Check along the tubing and if the air leak cannot be found, you might need to replace the CDU.
Monitor drainage. Typically drainage should not exceed >150-200cc/2 hours but it depends on hospital policy and on the surgeon. The amount of drainage should gradually decline. Monitor your vital signs!
Finally, don't accidentally knock it over