There are many ways to develop and maintain your child's social skills when homeschooled. Note that I said, "develop and maintain social skills." I did not say socialization, which is a different animal.
Socialization is the process of learning how to cope with social conventions, such was waiting in line, raising your hand to ask a question, and asking permission to go to the bathroom. Socialization is learning and following the rules to the game. Socialization is learning outside, social constructs. Socialization, in my experience, doesn't take much time or effort.
Social skills, on the other hand, relate to how your child interacts with other humans. Does your child bully other kids? Make them cry? Does your child show compassion and love? Can your child read body language and gauge a person's mood? Does your child know how to share? In my experience, social skills require the occasional bit of "theory" or "parental instruction" and a lot of practice. Resources for social skills include books at the library, library programs, programs at your local recreation center, homeschool co-ops, homeschool field trips, family interactions, interactions with people in stores, sports, lessons, special classes, and so much more.
Theory, or parental instruction
Parental instruction takes a small percentage of the time your child needs to work on his or her social skills, but it is important. Resources are sufficient.
Books: Go to your library or bookstore and do a search in the catalog. There are plenty of books that talk about different social skills. These tend to be storybooks for younger children. Look for phrases such as learning to share, sharing, being nice, bullying, what are friends, and the like.
"Lectures" with mom and dad: Every so often, my husband and I feel a need for direct parental involvement. (I consider reading the storybooks to the kids to be an indirect method of teaching social skills.) One of us will present a situation to the kids in the form of a little story. "Susie and Joe were playing in Susie's backyard. Joe wanted to be the fox in their game, but Susie also wanted to be a fox. Joe started crying and Susie called Joe mean." Now kids, what are some better ways that Joe and Susie could have handled this situation? Then, we go through a bunch of different methods with the kids. After that, we'll give them a couple more scenarios and have them answer us again.
Stop and breathe: The human brain isn't fully developed until well after legal adulthood. In the meantime, kids need crutches to help them. I regularly preach to my kids "stop and breathe." I tell them to stop and breathe before they react or say something when they're getting mad. Like the little lectures, we practice this.
Religious education and/or parables and/or fables: Whether or not you're religious, there is value in religious education. Bible stories and parables are excellent for this. If you're really against church, try parables. Aesop's fables have been around for thousands of years and they still have much value today. (Fables use animals to teach lessons.)
Practice situations Besides lessons from mom and dad, kids need lots of practice, and this is where being around other people helps.
Library programs: Check out your local library for special programs. My library has a monthly craft, and the kids need to sit at a table with other kids and share supplies. When babies, they went with me to story time, and they needed to stay with me and listen to the story. When my kids were toddler, they had a toddler story time and I didn't sit with them. They had to learn to sit and pay attention when mommy wasn't holding them. (This is more socialization than social skills, but valuable nonetheless.)
Rec center classes: My local rec center has classes on pottery, drama, yoga, and many other things. My daughter loves drama and has made a few friends that way. She also loved yoga and pottery. Both kids liked their class on gears and various animals.
Homeschool field trips: I am inundated with field trips for homeschooled kids in my area. I'm in Denver Metro though, and we have a big homeschooling community. Besides the co-op I'm involved in, there are many more, in my area and across the state. There are also several online academies that have field trips. The Denver Museum of Nature and Science has a homeschool day each time they put in a new exhibit. Field trips are nice because they are a bit more relaxed than class and the kids have more time to interact with each other.
Sports: Sports through private clubs or through your rec center provide opportunities for your children to interact with other children.
Trips to the store: Kids can develop social skills with adults, seniors, and younger children. A trip to a store is a good opportunity to watch your kids and see how they do.
Choirs: My daughter has been in the Colorado Children's Chorale for a few years. She loves it. While most of the time is focused on learning, the field trips allow her to interact with the other kids and make friends.
Even though my kids are homeschooled, they are well socialized and they have pretty good social skills. I am often complimented by strangers on the excellent behavior of my children, and on their ability to gauge people's emotions and body language. While neither of my kids have a ton of friends, they both have a couple of good friends. That's what it is all about, right?