Acetate (the conjugate base of acetic acid)* is converted into acetyl coenzyme A (acetyl CoA) by the enzyme acetyl CoA synthetase. This can enter the Krebs' cycle (also known as the tricarboxylic acid cycle), be incorporated into fatty acids, or go into other pathways. It is the reactions of the TCA cycle that make carbon dioxide from the carbon atoms within acetyl CoA. BTW acetaldehyde is also produced when one drinks ethanol. Ethanol is converted into acetaldehyde by alcohol dehydrogenase.
For your own interest, you might want to look into how ethylene glycol is metabolized. Veterinarians sometimes have to treat dogs who drink antifreeze, and oxidation of ethylene glycol produces oxalate, a very toxic compound.
*In the bloodstream for example (pH 7.4) acetate would be the main form. What do you think might be the case if acetate were found in the stomach?