Pitot pressure checks are accomplished with the pressure side of the tester only. Fully closing the crossbleed control valve will isolate the two sides.
When hooking up to the pitot probe don't forget to cover the bleed hole if it's got one. (Newer aircraft have static ports also. Normally the bleed hole is the one closest to the base of the probe.)
Before starting the electric pump or hand pumping the pressure handle, verify the pressure control valve is closed. If the valve is partially open, the airspeed indicator will tend to get pissed off, most likely because it was just driven from 0 knots to 500 knots+ in a split second. NOT GOOD.
Verify pressure bleed valve is closed.
Slowly begin to bring the pressure control open. By using small changes of the control valve, airspeed can be driven to the desired value.
I have found that using the electric pump to pressurize the pitot system is not needed. A few pumps of the pressure handle is more than enough of a tank charge to take all three systems on a aircraft the size of a DC-10 to the Barber Poll or Vmo needle (Vmo is short for velocity maximum operating limit).
It is good practice to go ahead and take airspeed over the Barber Poll needle to verify the overspeed warning system is operating normal. If the aircraft has two overspeed systems and both the Captain's and F/O's airspeeds are above Vmo, isolate the systems one at time by pulling the overspeed warning (clacker) circuit breakers. Newer aircraft use the air data computers for overspeed sensing.
Airspeed can be reduced to 0 knots by slowly opening the pressure bleed valve.
The point cannot be stressed hard enough. ALL VALVE ADJUSTMENTS FOR BOTH PITOT AND STATIC NEED TO BE DONE VERY SLOWLY. Air data instrumentation does not like to be blasted.
Leaks are sometimes noted while accomplishing a pitot check. More often than not, the problem is with the hose or adapter connected to the probe itself. Adjustment might be needed to assure a tight fit.
Our 767s got the winglets installed, and we now get overspeed conditions over mountainous areas, that didn't exist before. I think the ADC software isn't accounting for the difference, since it goes from .80 to .86 Vmo quickly, sounding the "overspeed" warning.