We have an older house that has some wall panelling in the bedrooms. I've painted the panelling and would like to add trim to all the edges of the panelling. Should the crown molding and the baseboard trims be installed first before the corner pieces?

i say put your corners in first then it will be easy to just cut in the rest of the trim

Corner? Where the base/crown meet the corner wall, or are you talking about the space from the bottom of the crown molding to the top of the base molding at the corners?

IF the former, then lay on your corners first, if the latter lay in crown and base molding first.