Begin by pulling the Docker image from Docker Hub using the Docker CLI. Use the `docker pull` command followed by the image name and tag. For example:
```bash
docker pull your-docker-image:latest
```
This command downloads the specified image and its dependencies to your local machine.

Once the image is pulled, run the Docker container locally. Use the `docker run` command with appropriate flags like `-d` for detached mode or `-it` for interactive mode, depending on your needs:
```bash
docker run -d --name your-container-name your-docker-image:latest
```
This starts the container and prepares it for interaction.

To access data inside the running container, use the `docker exec` command. This allows you to execute commands inside the container. For example, to list files:
```bash
docker exec -it your-container-name ls /path/to/data
```
Identify the data files or directories you need to move.

Use the `docker cp` command to copy data from the container to your host machine. This command requires the container name, the path to the data inside the container, and the destination path on your host:
```bash
docker cp your-container-name:/path/to/data /local/destination
```
This step transfers the necessary data from the container to your local environment.

Ensure MongoDB is installed and running on your host machine. You can use your package manager to install MongoDB. For example, on Ubuntu:
```bash
sudo apt update
sudo apt install -y mongodb
```
After installation, start the MongoDB service:
```bash
sudo systemctl start mongodb
```

Convert your data into a format suitable for MongoDB. Common formats include JSON or CSV. Use scripting languages like Python to transform the data if necessary. Example using Python for JSON:
```python
import json

# Convert your data to JSON format
data = {...}
with open('data.json', 'w') as f:
json.dump(data, f)
```

Use the `mongoimport` tool to import the prepared data file into your MongoDB database. Specify the database name, collection name, and data file path:
```bash
mongoimport --db your-database --collection your-collection --file /local/destination/data.json --jsonArray
```
This command inserts the data into the specified MongoDB collection, completing the transfer process.

By following these steps, you can successfully move data from a Docker Hub image to a MongoDB destination without using any third-party connectors or integrations.