Go to the Settings of your SendGrid account → API Keys → Create API Key.
Copy the API key.
Go back to Tilda, open the Site Settings → Forms → SendGrid. Enter the API key into the "SENDGRID API KEY" field, add the email you would like to receive captured data to, and your website domain name(s). Click "Activate".
Go back to the page with the form and open the Content panel of the block with the form.
Under "Connected Services", select the SENDGRID checkbox.
Publish the page. The contact form is ready!
If something fails to work, make sure that the URL of the page with the form matches the one specified in the form settings.