|(CC) alex_hanoco, Flickr.com.|
The first thing I make clear is that, unlike religions that have ministers, Humanist ministers are not authority figures - in the sense that they have some special knowledge or perception that others don't. In Humanism everyone is expected to think for themselves and not based their beliefs on authority.
To 'minister' means basically to administer some service. I have been certified by the American Humanist Association as a 'secular celebrant' and, as such, can legally perform weddings in the state of Texas (and do every so often). I can also provide funeral services, baby naming ceremonies, invocations, and conduct other ceremonies as needed. The AHA requires that registered celebrants have references and sponsorship from known and reliable people in the Humanist movement, that they demonstrate knowledge of Humanist philosophy in written essays, and that they fit some other requirements. In addition to ceremonial services, some celebrants also provide additional services such as counseling as needed. I can technically do this if I wanted to, but have not taken any courses in it so I refrain from doing so on personal principle. Nevertheless I can refer those in need.
Lastly, since many Humanist ministers are, of course, enthusiastic about Humanism, they tend to know a lot about it and be well read on it. Therefore, while not an 'authority figure' in the sense of being able to declare 'truth', a Humanist minister is usually a good person to answer questions about Humanism or have speak or write on Humanism.
Many people may not be religious, or they may be marrying someone of another religion and prefer a religiously neutral wedding or funeral. These people still want their event to be reverent, solemn, and have a sacred sense to it. Humanist ministers are therefore expected to be able to talk about important life events in ways that affirm the best in us, are touching, and yet do not reference the supernatural. As more people question their faith, these sorts of services have increased in demand.
As for a congregation, I am the former President of the Humanists of Houston, but my being a Humanist minister was incidental to that. Nevertheless, most secular celebrants serve the Humanists, atheists, agnostics, and freethinkers in their area, which largely includes members of the local organizations. I also consider my writings online to be a service of sorts, so it depends on one's definition of a congregation.
Here's a link where you can find a secular celebrant in your area:
The Humanist Society