Short answer: at grainer.com, search for the parts, buy it, and go pick it up at the nearest location to your area.
No, you’re not going to find capacitor, or AC fan motors, or AC contactor at homedepot, lowes, walmart, ACE hardware, and so on, they don’t have it.
You can call around locally nearest to your house but, those HVAC places around you probably not going to sell it to you, they will only sell it to contractor, like those people charge you an arm and a leg to fix your heating cooling system. You will be better off looking for local electrical supplies, such as grainer.com they’re the best, they have all the parts to your home AC and heating replacement parts. Keep in mind that it’s better for you to bring in the old parts when pick up the replacement parts to make sure it will work, it does not need to be 100% exact model or part#, but other specification match to the minimum requirement is good enough.
For example. I have Lennox AC unit located outside the house. Late it made loud humming noise. Found out the motor wasn’t spinning, although the compressor ran but very loud I guess due to the heat built up. Luckily I caught it on-time and shut down the AC.
I shut off the circuit breaker panel to the AC unit, also pulled out the shut off switch to the AC unit, then use the volt meter to ensure no more voltage or power feeding to the AC unit. In addition I also discharged all the capacitor by shorting it.
Next I removed the top cover where it hold the motor, disassemble enough to see the motor model #, specification and wires. Went online to grainer.com and search for the spec.
Since Grainer.com nearest location is an hour away, I went ahead and check those other parts on this 5 years old AC unit and buy all replacement parts at the same time. So I got the capacitor, additional ran capacitor for the new motor, and the contactor since this could go out in 5-10 years. So I removed all these items and search for the same spec replacement parts at grainer.com Drove an hour to pick up, and no they don’t ask if you’re contractor or personal, they might ask if you’re picking up for yourself or for your company though. It’s ok no worries, yourself is fine.
Went home and replaced it. Connect back the shutoff connector, switched the breaker back on. Turn on the AC controller on the thermostat, the AC unit kicked on 1 time for 1 sec, then off, then it kicked in again 1 second then off. Don’t worries, just leave it alone. Within 15 minutes or so, your controller thermostat will eventually trigger the contactor to turn on the AC. Give it sometime, don’t get scare thinking it doesn’t work. It will work just make sure you get all the wiring done correctly and you hear a momentary trigger to turn it on. It almost seems like it’s learning on how to behave properly with the new parts.