Hello, I recently installed a bathroom sink. This one has no hole for the overflow, and no holes for the faucets so basically only one hole for the drain. Is there a specific way to do this type of plumbing since the water takes a very long time to go down.

All sinks are required to have overflow. Overflow not only prevents overflowing water but also acts like a vent helping water to drain out faster. But I understand that some vessel sinks and/or designer sinks, like Porcher or Catalano, don't have overflows...

If you don't have overflow, you need to get drain that has no provision for overflow ( holes on side of the neck of the drain ). You can get those in Home Depot (Pegasus brand). They have "push" stopper as well. If you get drains from Grohe or Chigago than your sink will drain very slowly.

You have no hole for faucet. You will have install faucet on counter.