The term "half-sibling" is used to represent the family relationship of two or more children who share only one biological parent. One parent due to a divorce or widowhood, may remarry and a child or children are born to this new union. The original or oldest child and any new additions are considered half-siblings; a half-brother or half-sister. Compared to first-degree relatives such as a parent or siblings with the same two parents, half-siblings are considered second-degree relatives.
Another variation is a step-relative. The individual that a person remarries becomes a step-mother or step-father. In turn the blood-related children from each spouse becomes stepchildren to the new parent and a step-sibling to the other siblings.
When developing the family tree the core is the direct blood relatives; parents and grandparents. However, if there was a remarriage by any parent those new individuals must be added in. On the family tree, out from the blood parent goes a horizontal line to the other spouse with the information (names, dates). Down from that name will be any children of that union (the half-siblings). With those siblings would be their information including who they married and their children. Any half-siblings from this relationship should have a vertical line connecting them to the other half-siblings.
To assist in putting such family trees together is the Family Tree Templates site. It offers up a variety of different family tree charts, including one for adoptive parents. Additional sites which display the half-siblings and step-siblings is My Heritage which allows the researcher to fill in the blanks of a tree online and then print out the completed tree. There is also WikiTree site with several free printable diagrams to choose from to create a family tree especially for half-siblings.
The diagram offers a simple version of a family tree with a step-mother and half-siblings.