You must be on Salesforce Enterprise or higher.
Formstack Sync uses Oauth to authenticate with Salesforce.com.
Simply click the login button and follow the instructions. Use the "Login to Sandbox" button to connect with a Salesforce Sandbox.
Once connected, you can switch the connection by clicking the appropriate "Switch Accounts" button.
NOTE: If you are already logged into Salesforce when you click "Login to Salesforce", you will immediately see the "Success" screen above, without being asked to login to Salesforce again. If this happens, but you would prefer to login to Salesforce with a different account, then you will need to log out of Salesforce and then repeat the steps above.