If you have only ever shaved yourself over a sink, the barbershop version is a different experience. Here is what happens, in order.
Prep
You lean back and a hot towel goes over your face for a couple of minutes. This softens the hair and opens the skin so the razor can work without dragging. Pre-shave oil goes on next.
Lather and first pass
Warm lather is brushed on, which lifts the hair. The first razor pass goes with the grain. This removes most of the length without irritating the skin.
Second pass
More lather, then a second, more careful pass across or against the grain in the areas that need it. This is where the closeness comes from.
Finish
A cool towel closes everything down, followed by aftershave or balm. Total time is about thirty minutes.
If it is your first
Do not shave that morning; a day or two of growth gives the razor something to work with. Tell your barber if you are prone to razor bumps so they can adjust the passes.