Circle and soup is an excellent technique for conducting retrospectives. On the virtual or physical whiteboard, draw a large circle and then a smaller circle in the middle. Label the circle in the middle, "Things the team controls." Label the next circle, "Things the team influences." Finally, outside the boundary of the large circle, write, "The Soup."
Definitions:
Team Controls: This is the innermost circle and represents what the team can directly manage or change.
Team Influences: The middle circle represents what the team can persuade or influence to make changes happen to move ahead or improve the conditions.
The Soup: The outer circle represents items that can't be changed or that we've already adapted to within our work environment. These items are a constraint on the team's performance but require more significant influence to solve, which will take a long time before any fundamental changes within the soup will occur.
Have the team write out all the improvement ideas ahead or in the meeting. Get a bunch of them and then discuss which circle the team should place those ideas.
Take the ideas inside the "Team Controls" circle and prioritize them with the team. Pick the top 3-5. Save the rest. This isn't mission impossible. This whiteboard doesn't need to self-destruct after reading.
Put as stories in the backlog. Horrors! You should only put user stories in backlogs! Putting improvement ideas into the backlog, estimating them, developing acceptance criteria, and treating them similar (but not the same) as a user story allows for a few magical things to happen. Allocation of time and team focus being the biggest reason. You won't need the typical "AS A [blank] I NEED [blank} SO THAT [blank] format on the card. You'll need acceptance criteria to know if the card is done and how long you expect the card to take. Estimates are so helpful when trying to shoehorn the card into a sprint during spring planning.
Prioritize your process improvement cards along with all other cards (aka user stories). Yes, Virginia, there is a priority clause. Don't keep pushing off the process improvement ideas as unimportant. The team will need to step up and negotiate getting process improvement cards into a sprint.
Perfection Doesn't Happen Overnight
Unless you're a Greek God or wizard, everything isn't going to improve overnight. That's okay. The good news is you're on a journey to being a better team—step by step. You don't need to be perfect in the next sprint.
Oh, Scrum Master, Scrum Master! Wherefore art thou?
Remember those ideas that landed in the "Team Influences" circle? Your shiny dazzling Scrum Master will take those ideas and work with other Scrum Masters to play the influencing game. These types of process improvement ideas can't be done without the help of other teams. So break out the bribery, broadway showtimes, and smoke-filled dark rooms to negotiate an approach to these process improvement ideas. Chances are, these more significant process problems are affecting lots of other teams and not just yours.
It's Your Bag of Flaming Poop My Fearless Leaders
Remember the soup? Process improvement ideas that wind up on the fringe of the circles of soup require a policy or organizational change. Pass the improvement ideas up the chain of command—forewarning, dear reader. You will need to explain clearly and concisely the impact of NOT implementing the process improvement idea that is swimming in the soup AND the rationale of why it's so incredibly awesome - sell, sell, sell.