The Separation of Education and Socialization
And A little Bit Of What We Need To Focus
Follow the Path of Traditionally Schooled kids
Most local and public schools usually have tons of information weekly they give to parents regarding afterschool, enrichment and opportunities.
You can go capitalize on this yourself by doing the following:
1) Go into the local schools in your area and ask them for the weekly flyers they give out to their kids.
2) You can ask the parents of kids in your neighborhood that go to the local schools to share with you any activities, afterschool courses, etc for kids
Create Your Own Club
The homeschool group near where I live at has some very motivated parents. They've created 'teen' weekends at their homes and the teens can sign up monthly.
My kids love being able to interact with kids their age, goofing off, movie nights, gameplay nights and the max.
Don't Limit Your Kid's Group Of Friends
Many homeschoolers I've met over the years, tend to want to focus their kids interaction with other kids that are only being homeschooled. In my opinion, that's closing the door to your kid finding a potentially good friend.
Therefore, seek out kid focused social activities that are for all kids. Like recreational sports groups, clubs and afterschool enrichment.
The Key To Finding Friendships for Your Kid?
Consistency. Kids build friendships by consistently seeing and interacting with each other. Find activities that allow that and your kid will find good lasting friendships that way.