First, identify the Docker image containing the data you need. Use the Docker CLI to pull the image from Docker Hub to your local environment. Run the command:
```bash
docker pull
```
This command downloads the specified Docker image from Docker Hub to your local machine.

Start a container from the pulled image. This step involves running the Docker container so you can access its filesystem and data. Use the following command:
```bash
docker run --name my_container -d
```
Replace `` with the name of your image. The `-d` flag runs the container in detached mode, and `--name` assigns a name to the container.

Now, access the container's shell to locate and extract the data. Use the command:
```bash
docker exec -it my_container /bin/bash
```
This opens an interactive terminal session inside the running container, allowing you to navigate and find the data you need to export.

Once you've found the data inside the container, copy it to your host machine using the `docker cp` command. For example:
```bash
docker cp my_container:/path/to/data /local/destination
```
Replace `/path/to/data` with the actual path in the container and `/local/destination` with the destination path on your host machine.

Depending on the data format, you may need to transform it into a format suitable for MySQL import, such as CSV or SQL. This can be done using command-line tools like `sed`, `awk`, or simple scripting with Python or Bash to format the data appropriately.

Use MySQL's command-line tool to import the prepared data. If the data is in a CSV format, execute:
```bash
mysql -u username -p database_name -e "LOAD DATA LOCAL INFILE '/local/destination/data.csv' INTO TABLE table_name FIELDS TERMINATED BY ',' LINES TERMINATED BY '\n';"
```
Replace `username`, `database_name`, `table_name`, and `/local/destination/data.csv` with your MySQL username, database name, target table, and path to the data file, respectively.

After the import process, verify that the data has been accurately transferred. Use SQL queries to check the data in the MySQL database:
```sql
SELECT FROM table_name LIMIT 10;
```
This query checks the first few rows of the table to ensure the data has been imported correctly and is accessible in the MySQL environment. Adjust the query as necessary to perform further verification.