How Do I Provide Suggestions For Improvement Tactfully? (Ask Tigerhall)

Here's the scenario: you're collaborating with another team in your organization, and you're realising that there are some processes that could be improved. How do you provide feedback and suggestions to this team tactfully, without sounding like a know-it-all? This is the question a member of the Tigerhall community had, and Roberto Orlandi steps in with his advice.