Over the years of facilitating great retros, here's some top tips I have picked up along the way:
Silence is golden! This is probably my number one tip as I've seen product mangers/product owners/delivery managers run a retro and then spend most of it talking. This is an absolute no-no!! You're there to help make the conversation flow, ensure everyone has a chance to share their views and keep to time - it's time to put down the main character ambitions and let the product-engineering team have the limelight.
Don't forget to review previous actions If it's ticked off then it doesn't need much/if any discussion but anything which is outstanding or in progress should be briefly discussed to decide what next steps are needed. One important question to ask about any actions which are rolling over is "Do we still need to do this?" - actions shouldn't be blindly carried over.
Keep to time It's easy to run out of time in a retro, but it's your job as the facilitator to ensure you keep moving through the topics/parts of the session so that you can get the required actions and discussions out. Always keep a close eye on the time.
Note the actions and owners When you're noting down actions to take forward, ensure you write down who mentioned it and/or who's going to be responsible for it. This way you can easily tag them in the notes and any reminders.
Chase the actions The doing of the actions is a shared responsibility across the team, but as the facilitator it's your job to chase up throughout the sprint to ensure they're top of mind for people. I would chase a few days after the retro and then a few days before the next one to ensure people had time to tick them off. Using slack threads can be useful for this so people can post updates about their progress.
Ensure everyone has a voice This is one of the key roles of a facilitator. You should ensure that the session isn't dominated by the loudest person and even the quietest person gets a say. You can bring people into the conversation with phrases like "Thanks for your comments [X}, I'm keen to hear if [Y] agrees, disagrees or has a different perspective?" or "[Z] what's your view on this?", or '"[P] any insights to add in?".
Tailor the format to what you want to get out of it Before deciding on the retro theme I always think whether there's any burning questions for the team to address, any underlying tension, or any burning discussion points. I'll then choose a format which can be shaped to get to the heart of that. This ensures you get the best possible actions from the session.
Be prepared Ensure you know the format, what you're looking to get out of the session and have any accessories (post-its, pens etc). If you're spending time figuring out what's next or popping out to get bits and pieces then you're losing precious time for the group to be bonding, discussing and getting to actions.
Avoid the rabbit holes Another of your responsibilities as the facilitator is to help the group not fall down rabbit holes. A good way to avoid this is that if the group start getting into the weeds to put a pin in it and note down a task to have a meeting specifically on the topic "It sounds like this needs a wider group/more time to discuss/some additional context - I'll put some time in for us to discuss this".
Mix it up If you run the same retro format too often then it can feel repetitive and start to be less impactful for people. There are so many different formats that you can keep it fresh, even with limited prep time. That's why I've put so many formats on here!