Next, follow these directions for installing SQL Server Express. The default options are fine for most steps, but keep an eye out for these items:
On the 'Feature Selection' page (step 13 in the linked instructions), make sure to install Management Tools.
On the 'Database Engine Configuration - Account Provisioning' page (step 20 in the linked instructions), choose Mixed Mode Authentication. You will be prompted to create a strong password for connecting to the SQL instance you are installing. Make sure that you do not lose that password! By default, the username for that account will be 'sa'.