What is the device used to diagnose bad eletronic hardware?
The device is called an oscilloscope; it is used to measure voltage, not current.

The screen is much like a sheet of graph paper; with a graticule showing X and Y scales.  The Y (vertical) scale is for voltage, and the X (horizontal) scale is for a time base.  Thus the scope can show a signal varying in time across the screen.

Oscilloscopes originally used CRT (cathode ray tubes) to display the signal; now they all use LCDs.  The old scopes with the CRTs were very boxy, and also quite heavy.  The new LCD scopes are not very deep and quite lightweight.  Scopes usually have one, two, or four channels, with two channels probably being the most common.  This is a four channel LCD scope:



The first four BNC connectors along the bottom are used to connect to probes, with coaxial cables several feet long.  At the far end of the probe lead is a ground lead clip and a small sharp tip used to probe a circuit.  The probes also have a spring-loaded attachment to the tip to allow it to be temporarily clipped to a pin or wire on the circuit so the user doesn't have to hold it there.

The input circuits are very high impedance so as not to load down the circuit.

There are controls to vary the scale  for both the voltage and time, the Y scale typically from millivolts per division up to tens of volts per division.  The X scale can vary from nanoseconds per division to seconds per division.

There are also controls to set the position of the trace on the screen, both vertically and horizontally, and controls to select either AC or DC inputs, or ground.  The latter is used along with the vertical positioning control to set a baseline for a trace.

Another feature of a scope is the ability to set a "trigger", which can be used to stabilize a signal on the screen; the trigger is usually set to be a rising or falling signal at a particular voltage.  The trigger can be set to trigger on any of the scope channels, or (usually) an external trigger; that is the purpose of the fifth BNC connect on the scope image above.

Oscilloscopes are rated by their bandwidth.  The oscilloscopes ability to accurately display a signal will drop off rapidly as the frequency approaches the bandwidth of the scope.  Typical bandwidths of scopes are anywhere from 50 MHz to several hundred MHz and higher, with the price rising accordingly.

You can get a low end 2-channel 100 MHz scope for under $400, whereas a brand-name 4-channel 200 MHz scope might cost five times that much.