Hard time making new friends / Is shy

Before You Begin
Pause and breathe. Even if this shouldn't be happening... accept that it is and embrace it with composure and calmness.
Calmness is the only way forward because without calm, there is no possibility for receptiveness and connection. Your child won't give to you any more than they see from you.
Never forget that a strong connection is fundamental, as there will be no correction in them if there is no connection with you.
The Core Problem
Their own unique mix of shyness, social anxiety, a lack of social skills, fear of rejection, and/or difficulty initiating conversations.
What Will Make It Worse
Pushing the child into social situations they don't want to be in will increase their discomfort and make them want to avoid socializing entirely.
What The Child Needs
1. Belief in themselves: Help the child build self-confidence and belief in their ability to connect with others. Remind them of the traits in themselves that would make another person enjoy hanging out with them, and of people in their lives who they successfully became friends with.
2. To learn additional social skills: Talk about different ways to initiate conversations, keep them engaged and make connections through common interests. Role-play social situations with the child to help them practice these social skills.
3. Opportunities to socialize on their terms: Have the child decide what types of social situations they would look forward to. For some, it is seeing a movie with one other person, for another it could be going to an outdoor event in a group. Help them find their ideal circumstances and make it happen.
4. Positive reinforcement: Offer positive reinforcement and recognition when the child makes an effort to socialize or interact with others, even if it doesn't immediately lead to a strong friendship.
How To Have The Conversation With Your Child
Find a calm and private moment to initiate the conversation, where both you and the child can focus without distractions.
Begin the conversation with empathy, expressing understanding for any difficulties the child may have in making new friends. Let them know that it's okay to feel nervous or shy and that many children feel the same way. Encourage the child to share their feelings and thoughts about making new friends.
Share with them that friends can bring a sense of fun that they can't achieve by being alone or even with family, and you want them to have those experiences and feel that happiness.
Tell them that you are going to help them overcome this challenge on their terms with your support.
Next talk through the pointers under "What The Child Needs".
You don't have to discuss and practice everything all at once, especially if your child is starting to become disengaged in the conversation, but try to complete that checklist in the near term so they get a feeling of a new positive momentum in this area of their life.