There are several methods for testing an HID fixture's components, some of which require basic testing items - others require advanced test equipment.
Also, the type of Lamp will greatly affect the testing principles.
Basic tests may be performed with simple DVMs, Ohm Meters and Ammeters.
Ohm Meters are used to verify continuity through the Ballast's Windings, through the Lamp Holder and to check the Capacitor (if used) for short / open conditions.
Volt Meters are used to check input Line Voltage, Open Circuit Voltage and Lamp Voltage (disconnect Pulse Ignitors when used).
Ammeters are used to check for Input "Idle" currents, and Short Circuit current levels.
Simple "Non-Tester" tests may be performed with Incandescent Lamps or Mercury Vapor Lamps placed in the circuit.
Testing things like the output of a Pulse Ignitor requires something that can withstand the high voltage pulses, and display their frequency + amplitude and duratin.
An Oscilliscope works best.
Testing an HID Lamp requires a Regulated Power Supply type of a test device.
A normal Ohm Meter will read infinite Resistance (like an open circuit) on a good Lamp.
They are Arc Tubes, so testing them requires advanced methods (or simply try using the Lamp in a known operable fixture of equal type - this is a very efficient and low cost test method!).
Let me know what type of tests you plan to perform, and I can give you some testing examples, which do not require the use of hi $$$ testers.
Need to know Lamp type (LPS / Merc / Metal Halide probe start, or HPS / MH Pulse start), and how large (Wattage) of Lamps.
Can give test examples to cover nearly all scenarios, but do not require expensive testers.
The link that Scott (Electure) provided is really good - and may have all you need.
If not, or you have additional conserns / questions, let me/us know.