As GeoServer matures there are a variety of organizations that offer training. These range from online webinars, custom onsite classes, workshops at conferences, and other options. Some are introductions, other dive deep in to advanced GeoServer techniques. If you are offering training and want to promote it on this page then email the developers list and we can get you going.
Many of these organizations have more detail on the Commercial Support page, so read there for more information.
GeoSolutions (Italy) is a company with a strong commitment to providing innovative, robust, cost-effective geospatial solutions employing cutting edge technologies. They offer training on GeoServer as part of their services. You can find more information at this link.