Insert the crimped end of the adjustable duct into the plain end of the straight duct. Drill through the straight duct and the elbow duct inside with at least three sheet metal screws.
Seal the joint with mastic and a layer of fiberglass tape around the connection to form a seal -- alternatively, seal the joint with caulk.
Bend the adjustable elbow duct around the turn, then install the crimped end of your next straight duct into the elbow duct. Seal the two together in the same fashion as before.
Choose the correct elbow for your turn, as elbows for rectangular ducts are not adjustable. For example, to make a turn on the duct's horizontal axis, you need a "long-way" elbow. For a turn on the vertical axis, you need a "short-way" elbow.
Slide the plain end of your elbow duct into the S-hooks of a straight duct, then slide drive cleats into the channels to connect the two pieces.
Bend the ends of the duct down and over, once the drive cleats are secure, then seal the connection with mastic. Connect your next straight duct into the elbow using this same method of matching plain ends and S-hook ends.