Feel along the length of the duct for the nearest joint, which will be thicker than the rest of the duct. Use the utility knife to cut through any tape holding insulation on the duct. Do not cut through the duct itself. Peel the insulation back, exposing the joint.
Look at the joint to determine the type of connection -- if the joint is coated in a white sticky substance, apply a little extra force when removing the screws, but do not panic: this is a sealant called mastic. Remove any sheet metal screws. Loosen the clamps that are secured with screws.
Pull the joint apart with both hands. Avoid getting into the white, sticky mastic that coats the inside of many overlapping joints. Pull extra hard to loosen mastic; it will simply come apart with enough force. Look for additional screws if the duct doesn't feel like it will give.