Do a spell check and check all grammar before sending. It's a good idea to write your email in advance and then go away and read it again on a different day.
Ask someone else to proofread the email to make sure you haven't missed anything in spelling or grammar.
Send a test email to yourself and someone else if you can. Check that it looks right in your email client. Check every link that it directs to the correct URL.
Check every link that it is being directed to the correct URL (click on every one of them!). This includes all links you have manually inserted as well as sharing links.
Check that the header displays correctly in your email client and that it can be read without being cut off.
Check that the email is being sent from the correct sender and their email address is correct.
Check how your email looks on a mobile device. Remember that 66% of people are looking at their email on mobile devices.
Check that all personalisation is being displayed correctly. Eg. Dear Firstname.