One way is by including family members in a story. Here are a few ideas of how to insert them:
1. Part of backstory
Weave in small hints, or include flashbacks, which in some way tie in the past actions of a family member with a main character's present behavior. A mother who gave up a child for adoption, a father who cheated on his wife, or a sibling who received too little or too much attention, are some examples.
2. Immediate family interaction
What's happening in the here and now can be compelling. Some examples are a loving husband and wife, or the opposite, an incompatible couple, maybe squabbling siblings, or those who'll go out on a limb to help each other. One overused, yet still popular concept I often run into is the brother who gambles too much and the sibling who pays for the other's transgressions.
3. An important family event
One way to provide a glimpse of a character's nature is by depicting the death or funeral of a family member, either by natural or suspicious means. Lots of possibilities to depict grief, or perhaps jealousy over inheritance; or, on the other side of the coin, unexpected inherited debt.
Happy occasions, such as birthdays, anniversaries, weddings, are other ways to demonstrate how a character interacts with family members, be it for the good or bad.
Now it's your turn. Can you think of any other examples, or expand on one I've mentioned?