Under what circumstances can one republish a conference paper/presentation?
This varies by field. In (most) fields that have journal-based publications and no tradition of selective refereed conferences, it might be quite hard to publish a paper in a journal after it has appeared in some proceedings, without substantial changes.

In computer science, in which conference publication is the norm, it is expected that journal papers have first appeared in conference proceedings. This is especially true if the full paper does not fit in the page-limit of the conference proceedings, and proofs or other material had to be left out of the first publication. Typically you have to make some small changes between the conference and the journal version (i.e. include full proofs, include a fuller discussion of related and subsequent work, etc), but in CS, the delta between conference and journal version can be relatively minor.