Ensure you have `psql` (PostgreSQL command line tool) and Python installed on your system. `psql` is typically included with PostgreSQL installations, and Python is often pre-installed on many systems. If not, download and install them from their official websites.

Open your terminal or command prompt and connect to your PostgreSQL database using `psql`. Use the command:
```
psql -h hostname -U username -d database_name
```
Replace `hostname`, `username`, and `database_name` with your database's actual host, username, and database name.

Use the `COPY` command within `psql` to export data from a specific table to a CSV file. For example:
```sql
COPY (SELECT * FROM your_table_name) TO '/path/to/your_file.csv' WITH CSV HEADER;
```
Replace `your_table_name` with the name of your table and `/path/to/your_file.csv` with the desired local path for your CSV file.

Create a Python script to read the CSV file and convert it to a JSON format. Use the `csv` and `json` libraries in Python. Here is a basic script structure:
```python
import csv
import json

csv_file_path = '/path/to/your_file.csv'
json_file_path = '/path/to/your_file.json'

data = []

with open(csv_file_path, mode='r') as csv_file:
csv_reader = csv.DictReader(csv_file)
for row in csv_reader:
data.append(row)

with open(json_file_path, mode='w') as json_file:
json.dump(data, json_file, indent=4)
```

Execute the Python script in your terminal or command prompt by navigating to the script's directory and running:
```
python script_name.py
```
Ensure `script_name.py` is the name of your Python script. This execution will convert the CSV data to JSON format and save it locally.

Open the JSON file generated in your specified location to ensure the data has been correctly converted and saved. You can use any text editor or a JSON viewer to inspect the structure and content of the file.

If you need to perform this operation regularly, consider writing a shell or batch script to automate the entire process. The script can sequentially run the `psql` command, execute the Python script, and handle any error checking or logging as needed.

By following these steps, you can efficiently move data from a PostgreSQL database to a local JSON file without relying on any third-party connectors or integrations.