Friendships involving three people have never worked for me. In general, friendships involving three girl usually end badly; there are always two girl who are obviously closer and the odd one out was usually gossiped about or even alienated. I didn't have trouble finding one best friend, but that third missing piece loomed over me. Then I met a red haired girl who was hilarious on Twitter.
The key to the perfect trio is finding two people who seem like they would be your total opposite. Bear with me, the point I'm trying to make is that you need balance. Meeting two people who are your twins is so much fun at first, but I promise you'll quickly realize that two other people with your same personality is not a good thing. It's tricky finding two people with a balanced amount of things in common with you. I, for example am the most extroverted of my group. I'm loud and outspoken and my two best friends go with the flow and are homebodies, but it works because I have a little homebody in me and they both have a little "let's shot gun a beer at 8 a.m." in them. Being the opposite of your best friend in some areas in always fun because there are never dull moments or conversations.
Another huge component of friendships of three is communication. In friendships of three amongst girls, jealousy and insecurity is inevitable, especially if two of the girls were best friends before the third party was introduced to the group. Time together as a group is important, but one on one time with each friend is even more vital. Steer clear of surface talk and really get to know your best friends. Find out where they're from, what their home life is like, their favorite color, songs that make them happy and movies that make them cry.
My best friends compliment my personality in the best ways. I see a little of myself in both of them and them in me. Find people who you can un apologetically be yourself around. Find people who embrace you through the good and bad times. Finding your missing piece of the puzzle is difficult, but when you find it I promise it'll fit perfectly.