The nut on the larger spring in the pump pressure switch: Usually the larger nut in the pump pressure control switch adjusts the pump cut-on ("cut-in") AND pump cut-off pressures simultaneously. This is the left-hand spring (and nut) in our photo. That means that whatever the gap is between the cut-on pressure and the cut-off pressure, that gap is maintained, but the entire operating range of the pump is raised or lowered. Turning the large nut clockwise RAISES BOTH the cut-on and cut-off pressures. So turning the large nut clockwise shifts the whole operating pressure range of the pump UP to HIGHER pressures.
Conversely, turning the large nut counter-clockwise will lower the whole pump operating range. This is the simplest adjustment to make.
Photo (left) courtesy of a reader.
The nut atop the smaller spring in the pump pressure switch: this nut is used to narrow or widen the gap between the pump cut-on and pump cut-off pressures. This is the right-hand spring (and nut) in our photo).

Turning the small nut clockwise (tighter) will RAISE the CUT-OFF pressure, and vice versa, loosening or turning the nut counter-clockwise will lower the cut-off pressure. Watch out! If you loosen this nut too much you can set the cut-off pressure below the cut-on pressure and the pump will turn on and run forever (or until it burns up.)
Which nut to turn in the pump pressure switch control, and which direction to turn it, are usually visible on a label inside the pressure switch cover. Above we show photos of a common Square D water pump pressure control switch (Schneider Electric) and the label with pump control adjustment details. [Click to enlarge].
Here are Example Pump Pressure Switch Adjustment Instructions from Square -D Understanding how pump pressure control switches work and which way to turn which of the two nuts in the control can be confusing.
On a Square-D Pumptrol® 9013FSF-2 pump pressure switch, for example, Square D tells us that we

• Turn the Range Nut #1 (the larger spring and nut) clockwise (to the right or "down") to raise [both] cut-on and cut-off pressures. This is "tightening the nut down" against the spring. ("Rightie-tightie, leftie-loosie" as Mara Gieseke says to her kids). Thanks to reader Rise for this clarification.
  
  In other words, adjusting the pressure on this spring shifts the whole operating range of the switch up or down, but keeps the difference between cut-in and cut-out the same, whatever it happens to be (typically it's about 20 psi from the factory.)
  
  If you want the pump to turn ON (cut-in) sooner, that is, at a higher water pressure, turn the nut clockwise or "tighter".
  
  If you want the water pump to turn ON (cut-in) later, that is, at a lower water pressure, turn the nut counterclockwise or "looser".
  
  
• Turn the Differential Nut #2 (the smaller spring and nut) clockwise to raise the cut-out pressure.
  
  If you want the water pump to turn OFF (cut out or cut-off) at a higher water pressure, turn this nut clockwise or "tighter".
  
  If you want the water pump to turn OFF (cut out or cut-off) at a lower water pressure, turn this nut counter clockwise or "looser"
  
  Here is why the small nut is called the "Differential"