It turns out that this has already happened lots of times from developed nations over the past century.
Some examples to consider:
* Canada
* Australia
* New Zealand
* The Philippines
* Palau
* The Federated States of Micronesia
* The Marshall Islands
In all of these cases, the basic formula was some variation on the following:
* Form a stable local territorial/provincial government.
Ideally, one that the power from which you wish to secede considers to be in line with its views on how a stable government should be run. For example, if seceding from the U.S. or U.K. within the last roughly a century, having a stable democratic republican form of government certainly helps the argument for independence.
* Keep asking to take on more power/responsibility locally.
As your local government becomes more stable and increases its record of stability, continue asking the country from which you wish to secede for more local responsibility over running your territory's affairs, along with the power needed to carry out those responsibilities.
* Maintain good relations with the government from which you wish to secede.
Maintaining good relations certainly helps when arguing for independence. The government tends to be much more likely to grant local powers and tends to be much more amenable to granting independence when the local government is working with it in a friendly manner rather than antagonizing it in an adversarial manner. It also tends to be more likely to grant those powers when it trust the local government not to use those powers to suddenly start acting significantly against its interests.
* Develop an independent national identity and culture.
Of course, one of the key ingredients in getting independence is the local people actually wanting independence and beginning to think of themselves more as a separate nation and culture from the country from which secession is desired (if that's not already the case.) Over time, this also tends to get the rest of the people in the country from which you wish to secede to start thinking of you that way, too. 454
And it makes the argument that you can form a stable sovereign nation after independence much stronger.
* Ask for independence.
This step should be obvious, but, having completed the above steps, ask (ideally nicely) for independence. This often involves a significant degree of negotiating. It also sometimes involves initially being told no. When that happens, keep asking and keep negotiating. Going back to the first point, this is also often done in steps in order to ensure a smooth and stable transition of power. In some cases (Canada and Australia, for example,) asking for more and more local power may result in the local government eventually acting as a de facto sovereign nation well before the final vestiges of control by the government from which you are seceding are relinquished. 454