What have you found are effective ways to establish a decision making framework when you’re leading a new team? How much do you let develop naturally as opposed to taking deliberate steps?

I think there is particular value in establishing a specific-enough framework to give your team confidence in making decisions and taking action where appropriate. This frees up your time and creates an environment of trust with your team. I'm particularly fond of the "decision tree" framework that is described in the book Fierce Conversations by Susan Scott. In short, there are four types of decisions: leaf, branch, trunk, and root. Each type corresponds with the potential impact to the organization and increases the level of input from others and/or reporting before decisions are made. Establishing a team definition for each type would be a great start towards creating your own decision-making framework. See this link for more detail - https://www.techtello.com/decision-tree-for-making-better-decisions/

I'm curious whether you are a new leader to an existing team or whether the team is newly being formed?  If you are a new leader to an existing team, I would monitor how it functions and not necessarily impose a new decision-making framework if the team is successfully self-governing.  "If it ain't broke, don't fix it".  
If a new team is forming or an existing team is struggling with decision rights, discussing the approach to decision making is useful.  You want to create a collaborative environment yet, not so much so that the team seeks consensus on everything in a way that stymies progress.  The RACI model works where to define tasks and the types of decisions that will need to be made and assign people to be Responsible "do the work", Accountable "make sure it gets done", Consulted, and Informed. If we are talking about a decision, the Accountable person makes the final decision but ensures that they hear ALL voices before doing so. There can be any number of people with the R, the C, or the I but only 1 A in each row of the RACI.  Good luck!