Get scope probe or two. Not very much (around 20-50-60 each depending on bandwidth and brand type).
MUST, must get isolation transformer and "break" the ground on scope's side.
Cheers, Wizard
Just to help clarify the good advice given here by Wizard. What you will be doing is hooking up the two scope leads to live AC power for some of your measurements. Since the shield/ground terminal on the scope input (the outer ring of the BNC scope probe input receptacle) is attached to the metal frame and cabinet of the scope that entire instrument will become 'hot' with mains power during some tests if the shield lead is connected to a hot terminal. It is for this reason that extreme care must be employed when doing such measurements. The scope itself has to have isolated power. Power it from an isolation transformer rather than hooked directly to the mains supply. Make sure the third power cord pin (ground) is not connected to anything so the scope case can 'float'. Place the scope on a dry piece of plywood or other suitable insulator when using it for these measurements. Make sure you are wearing dry, rubber soled footwear and are also standing on an insulating surface. Avoid touching the case of the scope when making knob adjustments. This assumes the scope has insulating plastic knobs! Keep one hand in your back pocket so you cannot accidentally rest it on a grounded surface and electrocute yourself. BE AWARE AND BE CAREFUL. THINK THROUGH YOUR ACTIONS BEFORE MAKING THEM.......ALWAYS.
Limit your waveform tests to 120 volt circuits or less. Higher voltages start to create unexpected undesireable and not necessarily intuitive behaviors to the novice, plus are increasingly dangerous.
Even with a X1, X10 scope probe you will need to reduce the voltage to the probe with an additional series resistor placed in series with the probe input and the AC power terminal being examined. I suggest obtaining a 10 meg ohm, 1/2 watt resistor. This will reduce the voltage that the scope probe is subjected to saving it from possible burnout. Note that you will lose absolute voltage alibration accuracy but that is not what you are doing with the scope anyhow, you are more interested in the waveform shape which will not be compromised. We have voltmeters for voltage measurements.
If you are a novice in working with electricity try to find a experienced person who can mentor you in person or walk you through these tests the first time. Good idea to always have a buddy present when working with this stuff too!