Garry Bargsley rolls the dice:
In my experience, two options exist to get the desired result. One, create a new server, install the latest supported version of SQL Server, and migrate your data. Two, upgrade SQL Server on the existing server.
There are pros and cons to each of these options. My preference is to go with option number one as it allows you more flexibility in your migration plan. However, many smaller shops might not have the hardware resources for this option, so they are forced to option number two.
In-place upgrades have improved considerably, though certain ancillary services (like Machine Learning Services) have breaking changes between versions, so you may be forced into the first route regardless.