Just did this process. Bought my wife a newer used car at the dealership, they offered about half of its value on trade in of the KBB private party value, I said no thanks.
Paid my 15 year old daughter to clean the vehicle up nice, took a pile of pictures, the more the better, listed it on about 10 groups and Facebook marketplace, paid the extra $6 for 3 days of additional exposure, my listing appeared like an ad to other people. It showed that around 1,200 people clicked on and viewed my ad, worth it. In the end I talked to about 12 people over 2 weeks via messenger, first person that did show up paid cash and I sold it for $340 under top KBB value.
That was worth every minute of my time and effort to get several thousand dollars more out of it.
If you don't have Facebook, ask someone who does to list it for you and put your contact information on there.
If your talking about a vehicle around $10k or less, kept up and clean for is age, they sell fast.