A great time to let others know about your pronouns is when you are being introduced to them.
"Hi! My name is Jo and I use the pronouns Ze/Zir."
If you are at an event with name tags, add your pronouns under your name!
A helpful way to share your pronouns is through your email signature. Email signatures are lines of text automatically included at the end of every email you send. Many times people use signatures to display contact information and their pronouns. If you see that someone has included their personal pronouns in their email signature, take note of it.
To include an email signature within Microsoft Outlook:
Mistakes happen! What should you do when you accidentally use the wrong pronoun for someone? Perhaps one of your acquaintances has recently switched pronouns and you used their old pronouns. Maybe you guessed at someone's pronouns and were gently corrected by them. What do you do now?
As awkward as you may feel, the best solution is to acknowledge that you made the mistake, quickly apologize, and move on. Lingering on the issue may embarrass both parties.
Example: "He, whoops sorry, I meant to say They, are coming to the dinner."
Pronouns.org provides a great list of mis-pronoun-ed situational examples and suggests ways to quickly correct the issue.