Ensure you have Python and MySQL installed on your system. Python will be used to fetch data from the CoinAPI, and MySQL will store the fetched data. Install necessary Python packages like `requests` and `mysql-connector-python` using pip:
```
pip install requests mysql-connector-python
```

Visit the CoinAPI website and register for an API key. This key will be used to authenticate your requests. Make sure to store this key securely as it will be needed to access the API endpoints.

Before fetching data, design a schema in your MySQL database to store the CoinAPI data. Connect to your MySQL database using a client like MySQL Workbench or the command line and create necessary tables. For example:
```sql
CREATE DATABASE coin_data;
USE coin_data;
CREATE TABLE prices (
id INT AUTO_INCREMENT PRIMARY KEY,
symbol VARCHAR(10),
price DECIMAL(18, 8),
timestamp DATETIME
);
```

Write a Python script to make HTTP GET requests to the CoinAPI endpoints. Use the `requests` library to handle the API calls. Here is a basic example of how to fetch data:
```python
import requests

api_key = 'YOUR_COINAPI_KEY'
url = 'https://rest.coinapi.io/v1/exchangerate/BTC/USD'
headers = {'X-CoinAPI-Key': api_key}

response = requests.get(url, headers=headers)
data = response.json()
```

Once the data is fetched, parse the JSON response to extract the required information. Prepare this data for insertion into your MySQL database. Continuing from the previous example:
```python
symbol = data['asset_id_base']
price = data['rate']
timestamp = data['time']
```

Use the `mysql-connector-python` library to connect to your MySQL database and insert the data. Write a function to handle the connection and insertion:
```python
import mysql.connector

def insert_data(symbol, price, timestamp):
connection = mysql.connector.connect(
host='localhost',
user='your_user',
password='your_password',
database='coin_data'
)
cursor = connection.cursor()
insert_query = """
INSERT INTO prices (symbol, price, timestamp)
VALUES (%s, %s, %s)
"""
cursor.execute(insert_query, (symbol, price, timestamp))
connection.commit()
cursor.close()
connection.close()

insert_data(symbol, price, timestamp)
```

To keep your data up-to-date, automate the fetching and storing process using a scheduling tool like `cron` on Linux or Task Scheduler on Windows. Create a script or batch file that runs your Python script at regular intervals.

By following these steps, you can effectively move data from CoinAPI to a MySQL database without the need for third-party connectors or integrations.