These are normally classified by content, language, purpose and form.
Example
Learners analyse an example of a formal letter of complaint, looking at structure, set phrases, formality and purpose. They identify the key elements of this genre then produce their own examples based on this data.
In the classroom
Written genres that learners deal with in class include reports, news articles, letters of enquiry, stories, invitations, e-mails and poems. Spoken genres include presentations, speeches, interviews and informal conversation.
Further links:
https://www.teachingenglish.org.uk/article/student-presentations
https://www.teachingenglish.org.uk/article/developing-writing-skills-a-news-report
https://www.teachingenglish.org.uk/article/cheat-swindle-holidays