SharePoint 2013 has a new UI and a new way to Create Sites or Subsites.The option is now located in View all Site Contents instead of the settings menu.The option “Create Site” can only be added back to the settings menu using a Custom Action Feature created in Visual Studio See How to Add a Custom Action for Site Action or Settings menu in SharePoint 2013 to do this.
Lets look at the Steps to create a subiste
1. Click on Site Settings Wheel in the upper right corner of you site and select “Site Contents” page.
2. In the Site Contents Page, under Subsites heading click on “new subsite” Link.
3. When New SharePoint Site page appears, enter Title and Description, Web Site Address (URL), select a template, select Permissions and Navigation Inheritance.
4. Click Create when done. Below is the subsite that gets Created.