I recognize four ways to do it:
1) Commercial
The widest variety in formats and applications, ranging from intensive hard sell approaches to laid back and respectful; self censoring but often pushing the legal limits.
2) Listener Support
Often for upscale or specialty audiences, usually somewhat limited appeal and inducing a feeling of "membership" to supporters.
3) Subscription
Traditionally, automated jukeboxes for businesses such as Muzak or scamusica, but now with mass appeal systems including SiriusXM, some excellent personalities and absolutely zero non-program material.
4) Government
Tax or license based, censorship through omission only, such as songs with anti-policy lyrics, and usually annoying news on the top of each hour
I was going to include two more categories:
5) Religious funding, but concluded that these stations are either commercial or listener supported, both covered above, plus their programming always centers around narrow agendi.
6) College stations are more often than not for training students and having listeners who are students, rather than actually broadcasting to communities at large. One could conclude that their funding is derived from student tuitions.
This thread applies only to stations in western democracies where all types are allowed to co-exist.