I've not actually done this in practice. There is software that does that. The thing that will get you caught leaking sensitive information is when you have revealed something somewhere. If this newspaper publishes sensitive information you have access to, someone will see that your lemmy account was specifically asking about sending to that specific publisher.

Most journalists know how to protect sources. Some don't. Make sure you vet whoever you are communicating with.

How does one go about encrypting a message using a public key?

Find the place in your trusted email programms settings to add the recipients public key and select it when sending the mail.
If you want to be able to answer their questions you or identify yourself in follow up emails, you should also generate your own key.

Also should I use a burner email ID to send the encrypted message to guardian?

Anyone spying on you will only be able to see that you contacted the guardian but not what you told them. Having a burner would mean someone sees you contacting the burner service and than the newspaper. That said you should probably make a new email for it but I don't know what exactly you understand as a burner email.