Before you begin, identify the type of iterable you have. An iterable can be a list, tuple, set, or any object that implements the `__iter__()` method. Ensure you know the structure and content of the data in the iterable to effectively transform it into JSON format.

Use Python’s built-in libraries to handle data conversion and file operations. You will need to import the `json` module to convert Python objects to JSON format and the `os` module if you need to handle file paths.

```python
import json
```

Ensure that the data within your iterable is compatible with JSON format. JSON supports data types such as strings, numbers, lists, dictionaries, and booleans. Convert any non-compatible types (like custom objects) into dictionaries or lists.

```python
data = [item.to_dict() for item in iterable] # Assuming iterable contains objects with a to_dict() method
```

Use the `json.dumps()` function to convert your prepared Python data into a JSON-formatted string. This function serializes the Python object to a JSON string.

```python
json_data = json.dumps(data, indent=4)
```

Decide where you want to store the JSON file on your local system. Define a file path as a string. Ensure the directory exists or create it if necessary.

```python
file_path = 'path/to/your/file.json'
```

Open the specified file path in write mode and use the `write()` method to save the JSON data. Ensure you handle file operations safely using a `with` statement to automatically close the file afterward.

```python
with open(file_path, 'w') as json_file:
json_file.write(json_data)
```

After writing the data, open the JSON file to check that the content is correctly formatted and complete. You can manually open the file or implement a small script to read the JSON file and print its contents.

```python
with open(file_path, 'r') as json_file:
loaded_data = json.load(json_file)
print(loaded_data)
```

By following these steps, you can successfully move data from an iterable to a local JSON file using Python’s built-in capabilities, without the need for external libraries or integrations.