I can think of two anime that fit your description. One is Comic Party which I've not seen too much of, but seems to be about a guy getting dragged to an anime convention and really winds up getting into it and trying to make his own manga.
Another, and probably the most famous, is Otaku no Video by Gainax, same studio that created Evangelion, FLCL and others. It's basically a dramatic anime style telling of the history of Gainax itself (which was started by anime fans), as well as a documentary featuring footage and interviews with fans in Japan.
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