How do massively wide trucks/loads get around when not on the highway?

The transport company maps out preferred path of travel.

This path is usually submitted to the state transportation authority along with city or county whose roads will also be used (multiple state departments if crossing state lines). Details of the trip, equipment used and support vehicles are described in the permit (The state will have general guidelines already laid out in their permitting literature, and is generally similar across state lines.)

The permit is reviewed, and a timeline is established between all jurisdictions. When the transport can operate, what roads will be used, what support vehicles, does it require a police escort… and lastly, are there any modifications to public property that is required to transport your object.

Back to your question. Local cities will establish a route that allows the transport to occur. They will also decide if your support crews and vehicles can direct traffic as needed or if local police will do this for you. If modifications to public property is needed it is likely that this is taken care on many months prior to your transport.

Things that are multi lanes wide tend be moved at or near 3am when traffic is the least, if possible.

Very large objects can take a year or more of planning and approvals, but most take about a month to setup.