This is the easiest and least costly process—actually there is no added cost for this process. Simply remove the mask clearances from the vias you wish to have tented. Tenting a via simply means to cover the annular ring and via hole with solder mask. No special steps are taken to ensure the hole opening remains closed. Tenting a via will sometimes result in the hole remaining covered but it isn't guaranteed. Smaller diameter vias (12mil diameter or less) have the best chance of remaining closed. The main purpose for tenting shouldn't be to close the opening of a hole but rather, cover the annular ring to prevent exposure to the elements and reduce accidental shorting or contact with the circuit.
TIP: If you are tenting some of the vias in your design, always make a fabrication note either in a readme.txt file or Gerber fab drawing so we know you have intentionally removed the mask clearances from some of your vias. Otherwise we may put the order on an engineering hold to verify your intention.