Hi there
When car shopping I use:
Autotrader
Pistonheads
Collecting Cars
Manner Park Classics
CarandClassic - also good for finding cars in EU
Motors UK
Facebook Market place
Ebay
Gumtree
Manufacturers used car for sale sections
Join various FB groups in your country for model you looking for and ask if anyone is considering selling soon, to try and grab an off market car cheap
Various auction sites etc.
for USA bringatrailor is a good one.
When I am selling a car:
Pistonheads (its free for me and good success rate)
FB market place (also free and very effective for cars sub 20k)
Various FB / Insta / Forum groups for specific car models and can be quite successful as your targeting the niche.
I will always try to intercept a car before it goes to trade and buy privately, it is more risky as zero warranty (unless within warranty) but at same time can easily save yourself 10-30% of the price, if you want some comeback then of course buy from a dealership.