There are multiple ways to change the appearance, or theme, of an infobox, but the complexity of the task depends mainly on the type of infobox being used.
Portable infoboxes[]
Portable infoboxes can be both the easiest to theme and, conceivably, the hardest to theme. This is because they have a default theme based on the colors chosen in the theme designer. While these can be changed or improved using MediaWiki:Common.css, the only users allowed to change it are admins/bureaucrats.
Theme gallery[]
Steven Universe example
My Singing Monster example
Classic infoboxes[]
The appearance of classic infoboxes can be changed by any user by relying on inline styling, although some more complex changes can only be achieved by admins.