You can find some good examples of JoinBuilder in the unit tests here. To run the join query you need to convert the builder to SQL and then pass it to Select, like this:
var sql = jn.ToSql();
var items = con.Select<SchoolYearPeriod>(sql);
You can also use the join builder in conjunction with the expression visitor, so you can create complex WHERE filters after the join, like this:
SqlExpressionVisitor<SchoolYearPeriod> ev = Db.CreateExpression<SchoolYearPeriod>();
ev.SelectExpression = join.ToSql();
ev.Where(syp => syp.MyDate > DateTime.Now);