The connection of vias in multilayer PCB's used to be done via (no pun intended) electroless plating, but that process is a bit fiddly, demanding extra precleaning and postcleaning, and use and disposal of hazardous chemicals, such as chromium compounds. You can still buy an electroless plating kit, for US$150 and up, but the solutions have limited shelf life and contain various hazardous compounds.
Commercially, electroless deposition has largely been replaced by the black hole process, so-called because a thin layer of black conductive carbon is deposited in the via, then plated with copper.
An individual might find conductive ink an alternative method for connecting vias. This can be automated, as in this video. Conductive ink can be found for ~US$120 for 50 grams. Also, see this paper on filling vias with conductive copper paste.