When you turn the ignition key and you hear a clicking sound, or after a few seconds of cranking, the starter runs sluggishly and cannot start the engine, you know you have a starter problem.
First of all, you can damage a starter by continuous cranking, because the starter heats up very rapidly. After cranking for a half minute, let it rest for a couple minutes to cool off a bit. The starting system imay not be the problem if there was a drastic drop in outside temperature. In that case, also check the car for ignition or fuel system problems.
The first impulse is to grab jumper cables, though this will not help if the crankcase oil is like molasses (in theory a "block heater" should prevent this"), or the engine is tight or seized, then the engine cannot crank fast enough, even with normal battery amperage. Boosting from another source may provide additional amperage but can also damage the starter.
Be careful jump starting a modern car, with electronics and computers onboard. These electronic components are vulnerable to voltage spikes. Before jump starting a late model vehicle, you should read the Owner's Manuals, which typically have specific instructions for jump starting, or recommendations not to.
You can diagnose several starting system problems without any tools or measuring equipment.
Turn on the headlights and start cranking. If lights go out, you probably have a poor battery cable connection that is impeding the flow of current.
If headlights continue to shine brightly and nothing happens, voltage is probably not reaching the starter. There may be a problem with the park/neutral or ignition circuit switches.
If lights go dim and the cranking action is sluggish, first suspect a low battery. Starting problems in cold weather, when no problems existed in summer are often due to a weak battery. Sub-zero temperatures can cut a battery's amperage output by more than half.