Organic carbonates are not prepared from inorganic carbonate salts.  
Two main routes to carbonate esters are practiced: the reaction of an alcohol (or phenol) with phosgene (phosgenation), and the reaction of an alcohol with carbon monoxide and an oxidizer (oxidative carbonylation).  Other carbonate esters may subsequently be prepared by transesterification.
In principle carbonate esters can be prepared by direct condensation of methanol and carbon dioxide.  The reaction is however thermodynamically unfavorable. A selective membrane can be used to separate the water from the reaction mixture and increase the yield.