If you haven't just created an account or previously chosen to have your log in details remembered, then when you launch SpeedScriber, you'll see the welcome screen with a field to enter your email address. Click Continue and if there is an account on that email address then you'll see this log in screen:
Enter your email address and password then click the Log In button.
The Remember Me checkbox is disabled by default. Enabling it will securely store your log in details on the Mac and automatically log you in when the app is next launched. If you are using SpeedScriber on a shared Mac, you will probably want to leave this option disabled.
If you cannot remember your password, then click the Forgot Password button and enter your email address. A temporary password will be emailed to you, which you should use for the next log in and then change.