When I first took my son out of school, the first question everyone asked was "what will you do about socialisation? He won't have any friends."
My answer was that he didn't have friends at school, and I didn't see how it could be any worse if he stayed at home. I feel strongly that being without a friend amongst a class of children is even more lonely than being on your own.
We joined Education Otherwise, and went along to any activities that seemed suitable. As my son has ADD and dyspraxia, he could be over boisterous, loud, excitable, and clumsy, often crashing into people or pushing them over. Making friends was hard, and he was very anxious around other children. When he got anxious he got louder, rougher, and lost his temper more easily, none of which helped him to make friends.
I tried a number of things to help him. At home I played with him as much as possible, to build up the play skills that he needed. After a stressful time at school, we'd got into tense habits with each other and we both needed to learn how to have fun together again. I tried not to direct his play, but follow his lead and even join in silly things with him - the kind of things that made him laugh, but that used to make me anxious because I imagined him doing them at school and getting into trouble.
He had one friend that we could invite to play. This little girl was very forgiving and great fun. When she first used to visit I had loads of activities available; making play dough, icing biscuits, outings ,and joined in with everything they did so that I could support him and help him keep control. As they got used to each other they developed games that they wanted to play together and I could withdraw. This took a long time but has been very satisfying.
At organised activities I learned never to stay too long, so we tried to leave before he had time to get stressed or bored. I found another advantage to being home educated.If he was having a bad day, we didn't go to activities so his new acquaintances didn't have to see him at less than his best. Also, children who might have found him hard work for long periods were able to enjoy his company in short bursts. He began to make some new relationships.
We were lucky to meet a very understanding lady with a son the same age as mine.The two boys were drawn to each other, but liable to get very frustrated with each other. My friend didn't judge or get cross when the children fell out. When things went wrong between her child and mine we were careful not to blame either child but to sympathise with both peoples hurt feelings, and support them both in moving on from the problem.
I also found it useful to practice strategies for joining a group of children. He learned to watch the game first, and ask to join in. If this didn't work, instead of trying to force his way in, I have tried to teach him to come to me so that we could think of something fun to play together. More often than not other children then come wanting to join in. It was worth being the only silly adult running around with the children to see him finding a place within the group. It is still hard for him at times.
Although the other children accept him now, he is aware that few of them choose him as their partner. I hope that this too will change for him with time. He now has a "special friend" who doesn't live very near to us, but whose pleasure in my son's company means that it is worth a longish journey to meet up.