How do you introduce your own new girlfriend or new boyfriend to your 10 year old child?

Fun activity. Think of a fun activity that your 10 year old likes that can be done with other people. (bike ride, bowling, sports, etc). Let your child know you have a friend who also likes that activity and you have invited them to join you. Center the conversation about the child and the activity, not your relationship with adult friend. Do this a couple of times over several weeks and let things develop.