I lucked out.
When my older daughter started Kindergarten, it just so happened that she and a group of about 6 other kids all got together and played in the schoolyard while us parents chatted. Over time and changes that entire group was whittled down to 2: my daughter and her best friend. It just so happens that her BFF's mother is a darling woman with whom I have at least a million things in common. We're about 10 years apart in age, and we often joke about it. I consider her MY BFF.
Added bonus: both of our husbands are men who are shy and really have a hard time making friends...guess what? THEY'RE now friends too!
Aside of that, while she and her little sister are still small, whenever they are invited to a birthday party, I go with them. I chat up the parents and help with the party. I'm friendly with most of the other parents, but no real friendships were formed. A few, if they invite her over, I'm OK with. Some (like the family who was watching "Goodfellas" in the middle of their 6-year-old's birthday party) not so much.