If the container sits entirely on private property, like a driveway or a building's own lot, the city generally stays out of it. The moment any part of it touches the public sidewalk, parkway, or roadway, you need an approved permit first.
West Hollywood calls it an encroachment permit, and the city lists construction debris container staging among the activities it covers. It has to be approved before the bin arrives, not after.
Plan the calendar carefully. The city says a typical review runs about 10 business days per submission, and a resubmittal takes about the same again. A permit application normally needs proof of insurance naming the city, a contractor license, a city business tax certificate, a traffic control plan, and a construction plan. Once it's issued, you collect "No Parking" signs and post them before the drop.
Also worth knowing: moving and storage containers, construction trailers, portable toilets, and overnight storage of equipment or materials are not allowed in the public right-of-way at all. City Hall is at 8300 Santa Monica Boulevard and the main line is 323-848-6400.
There's one more rule that sets this city apart. West Hollywood only lets haulers it has approved place construction containers, and mixed demolition debris has to leave with a company the city permits to operate here. That affects how a booking is arranged, so your account manager will confirm exactly how the rule applies to your address and your project before anything is scheduled.