I've bought used tools without ever powering them up. This $40 table saw would have been in that category. I wouldn't have wasted time to even power it up. "$30 bucks untested".
Anyway, here's a draft:
1,2,3,...) check area for safety. Be careful. You're working in someone else's space, a stranger. When you unplug the cord tell the seller you are doing that, then keep an eye on the seller that they don't plug in the saw when your doing things with the saw/motor.
4) unplug the table saw. verify the correct cord was unplugged by trying to power up the saw.
5) take the belt off
6) wiggle hard the motor pulley. shouldn't be any play
7) spin the motor pulley. should spin numerous times before slowing down, and there shouldn't be any noise whatsoever, not even faint.
8) wiggle hard the table saw pulley. shouldn't be any play
9) spin the blade. should spin numerous times and there shouldn't be any noise whatsoever, not even faint.
10) put on gloves
11) wiggle the blade. shouldn't be any wiggle.
12) inspect the power cord for cracked insulation etc
13) with belt off, plug in the cord.
14) if you have an ohm meter, test the motor housing and table saw for shorts.
15) verify the area is safe powering up the saw, no kids, no dogs, nothing on the floor to trip over, there is a clear path to back away from the saw, table saw isn't wobbly, is off it's casters or they're locked
16) power up.
17) test for shorts again
18) listen. should be quiet and vibration free. definitely no high pitch
19) power off. motor should spin for a long time
20) unplug. verify the correct cord was unplugged by trying to power up the saw.
21) put the belt on.
22) remove the blade, the washers and the nut
23) verify the area is safe powering up the saw, no kids, no dogs, nothing on the floor to trip over, there is a clear path to back away from the saw, table saw isn't wobbly, is off it's casters or they're locked
24) plug in,
25) power up. there should only be low humming, no high pitched noise.
26) power off. unplug.
verify the correct cord was unplugged by trying to power up the saw.