First, log in to your Google Cloud Console and create a new project or select an existing one. Ensure that billing is enabled for the project, as BigQuery requires an active billing account. Navigate to the "BigQuery" section and activate the API if it is not already enabled.

Visit the Coin API website and sign up for an account if you haven't already. Once registered, navigate to the API section to generate an API key. This key will be used to authenticate your requests to the Coin API.

Create a Python script using the `requests` library to fetch data from the Coin API. Use the API key obtained in step 2 for authentication. For example:
```python
import requests

api_key = 'YOUR_COIN_API_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()
```

Process the data fetched from the Coin API into a format suitable for BigQuery. Typically, this involves converting the data into a JSON format or a CSV format. Ensure that the data types align with BigQuery's supported data types. For JSON, ensure that the structure is flat or can be easily parsed.

In the Google Cloud Console, navigate to BigQuery. Create a new dataset if one doesn't exist by clicking on "Create dataset,"� and specify the dataset ID. Within the dataset, create a new table with the appropriate schema that matches the data you are importing.

Install the Google Cloud SDK on your local machine if it's not already installed. Use the `bq` command-line tool to upload the data file. For example, if your data is in a JSON file:
```bash
bq load --source_format=NEWLINE_DELIMITED_JSON your_dataset.your_table /path/to/your/data.json
```
Ensure that the data types in your JSON file match the schema of the BigQuery table.

To automate the data fetching and uploading process, consider using a task scheduler like `cron` on Unix-based systems or Task Scheduler on Windows. Create a script that runs your Python data-fetching script and then executes the `bq load` command. Schedule it to run at regular intervals to keep your BigQuery data updated.

By following these steps, you can effectively move data from the Coin API to BigQuery without relying on third-party connectors or integrations.