I would like to open my Word documents in the browser and not in the program Word. I have Office 2013, I don't know if this matters. How do I go about doing this?
Office Web Apps are optional in SharePoint 2013 installations. Assuming on-premises (not Office 365), your installation may not have Office Web Apps installed or configured correctly (e. g. http://msdn.microsoft.com/en-us/subscriptions/ff431687.aspx).
For Office 365 it depends on the subscription level.