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 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:Wikia.css, the only users allowed to change it are admins/bureaucrats.
Portable infoboxes also come with an optional "Europa" theme that can be enabled by admins using Special:Wikifeatures. When the feature is activated, it will change the default appearance of portable infoboxes, such as making the alignment of the heading or title centered and changing the background colours.
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.