A logo is used by businesses to help their customers remember their brand. It is also used to unify the company and it's employees, giving them a symbol of what they are working for. A reminder of the company motto & vision.
Thinking of world history- families used to have a crest, a brand, or a symbol to show owner ship of land, livestock, or property. The modern family might not use it the same way, but a family logo could do a lot of the same things: help give identity and unity to family members & reinforce the family motto and values.
Typically, logo design takes a lot of research and considers the company image and it's target market. A family logo doesn't have the same restraints. It's for you and your family. It could be anything you want!
You don't need to be a graphic designer to have a family logo. Just go back to your plan and vision board and motto and decide on images or thoughts you want to incorporate into your family logo. There are a lot of free clip art sites, fonts and drawing programs that you could use to put it together.
For our family logo, we decided we would use our initial- C, the number of people in our household- 8, and try to incorporate of family motto of "choose happy. do happy. be happy." I tend to create logos that are typographic and simple. I always try to make the main logo and then a smaller symbol that can be used for smaller applications. This is what I came up with for us:
The top image is the symbol and the bottom the whole version of the logo. The symbol incorporates the C, 8, and turn it on its side and it's a smiley face. I made a couple more generic ones to show you want you can put together with just fonts & clip art:
If you need an editing program, try these online options:
Vector files- Aviary.com
Image files- Picnik.com, Pixlr.com
With the popularity of digital scrapbooking, there are a ton of free resources on the web. Here are a few places to check for fun free images and fonts:
Just Something I Made (the vintage bird graphics above are from here. Cathe has a lot of great free downloads- and all around great ideas)
The Graphics Fairy