Selling Confused

How does trading and selling villagers work? I am newer to this website and wasn't aware people traded and sold villagers????

When a villager is moving out, someone puts up a trade offer for another villager that they want or if they want bells or TBT

So say Stitches was moving out of my town.
I would say [FT] Stitches [LF] Bells or Chrissy
Then one person would come over and grab stitches and then I would go over and grab Chrissy.

Thank you! I understand that now. That is what I figured but I wasn't 100% sure.