If you're looking to put your family tree online for Family History Month, you have a few free options.
You can create a Ancestry Family Tree without a paid subscription to Ancestry.com. Create a free account here and then start adding names to your tree! You will not be able to attach documents to your tree like you would a paid account but you can organize all of those names, branches, and dates. You can even add photographs to your tree.
Ancestry Member Trees are searchable in Ancestry's database or you can adjust the privacy settings so the tree is only visible to you.
MyHeritage allows you to create a free family website and family trees. You can add documentation, photographs, calendars and family events. There are multiple options for adding all kinds of biographical data to your entries. You can also invite other family members to view and share information on the site or in the tree. There is also free family tree software that you can download to your computer if you're not interested in working through a web browser.