Summarize:

It's the white ghost outlined on a yellow background. It's the top line on this page. You'll need this to continue with the password reset process. It's below the password entry field. This option will send a password rest link to your Snapchat-registered email address. It's above the "I'm not a robot" box.  This option is here to ensure that you're a human user and not a spam program. You may need to participate in a minigame like selecting every square in a grid that contains a certain image and then tapping Verify. It's at the bottom of the page. After tapping Submit, Snapchat will send you a verification email.  Its sender should be "Team Snapchat", and the subject of the email will be "Snapchat Password Reset". If you don't see the email, try looking in your email provider's Spam folder (also check the Updates folder if you're using Gmail). It's the middle of the email from Snapchat. They'll need to match in order for you to continue. Your Snapchat password has been successfully reset! Now you can log into your Snapchat account.
Open the Snapchat app. Tap the "Username or Email" field. Type in your username or email address. Tap Forgot your password?. Tap via Email. Tap the Email field. Type in your Snapchat email address. Tap the box next to "I'm not a robot". Tap Submit. Open your email address. Open the password reset email. Tap the reset link. Type in a new password twice. Tap Change Password.