Carboxylation is a standard conversion in organic chemistry. Specifically carbonation (i.e. carboxylation) of Grignard reagents and organolithium compounds is a classic way to convert organic halides into carboxylic acids.
Sodium salicylate, precursor to aspirin, is commercially prepared by treating sodium phenolate (the sodium salt of phenol) with carbon dioxide at high pressure (100 atm) and high temperature (390 K) – a method known as the Kolbe-Schmitt reaction. Acidification of the resulting salicylate salt gives salicylic acid.
Many detailed procedures are described in the journal Organic Syntheses.
Carboxylation catalysts include N-Heterocyclic carbenes  and catalysts based on silver.