Dryer vent caps are deliberately lightweight so they'll open easily, but this flimsiness also means they'll break easily. The caps, especially the type with multiple small flaps, also clog easily with lint. (Avoid this type unless you're conscientious about cleaning it.)
To replace an old vent cap, first pull apart the duct at the last joint inside the house. If they don't pull apart easily, look for small screws holding the sections of pipe together. Next, remove the screws or nails used to attach the cap to the siding and cut through the caulk around the edges (Photo 1). Pull out the cap, scrape away old caulk and dirt, and then wipe the siding clean so new caulk will stick.
Cut the new vent pipe to the same length as the old one, then slide it through the wall. Screw the cap to the siding and caulk around the edges with paintable caulk.
Finally, join the old duct inside the house to the new vent (Photo 2). Vent caps are available at home centers.