See also the official documentation:
Help Center > Members Manual > Understanding Groups.io accounts > Logging in to your account

• I Don't Have A Password
  • To log in without a password, go to the Log In page and click the Email me a link to log in button. Once you enter your email address, you'll immediately be sent an email with a link that will automatically log you into Groups.io. You will stay logged in for up to 30 days, unless you log out.
  • Need help logging in? See https://groups.io/g/GroupManagersForum/wiki/Logging-In.
    
    
• I Forgot My Password
  • Follow steps in "I Don't Have A Password", then:
    • You can then set a password if you wish, or you can continue to use the Email me a link to log in function to log in when needed.
      
      
• Changing your password - see instructions on this wiki page.
  
  
• For a complete how-to, see this wiki page for a complete How-To: login, setting password, etc.