Begin by accessing the GitLab instance you wish to extract data from. Navigate to the GitLab API documentation to understand the endpoints and data structures. Ensure you have the necessary permissions and an API access token, which you can create from the GitLab user settings under Access Tokens.

Formulate an API request to fetch the data you need. For example, if you want to retrieve project data, you would use an endpoint like `https://gitlab.com/api/v4/projects`. Use a tool like `curl` or any programming language's HTTP library to construct this request. Don’t forget to include your API token in the request headers for authentication.

Write a script in a language such as Python that can send your API request and capture the response. Use the `requests` library in Python to simplify this process. Your script should parse the JSON response and store it in a format that can be easily exported, such as a CSV file.

```python
import requests
import csv

headers = {"PRIVATE-TOKEN": "your_access_token"}
response = requests.get("https://gitlab.com/api/v4/projects", headers=headers)
data = response.json()

with open('gitlab_data.csv', 'w', newline='') as file:
writer = csv.writer(file)
writer.writerow(data[0].keys()) # Write headers
for item in data:
writer.writerow(item.values())
```

Once you have your CSV file, you may need to clean or format it to ensure compatibility with Google Sheets. Check for any special characters or formatting issues that might need correction. Make sure your CSV adheres to UTF-8 encoding to avoid any import issues.

Manually upload your CSV file to Google Drive. Navigate to your Google Drive, click on the "New" button, and select "File upload." Choose your CSV file from your local directory and upload it to Google Drive.

Open Google Sheets and create a new spreadsheet. Use the "File" menu, select "Import," and choose "Upload." Select the CSV file from your Google Drive. When prompted, select "Replace spreadsheet" to import the CSV data into your Google Sheets directly, or append to an existing sheet if required.

If you need to perform this operation regularly, consider automating it using Google Apps Script. Write a script that can download the CSV from Google Drive and import it into the desired Google Sheet. Schedule this script to run at your required frequency using Google Apps Script’s trigger functionality.

```javascript
function importCSVFromDrive() {
var file = DriveApp.getFilesByName('gitlab_data.csv').next();
var csvData = Utilities.parseCsv(file.getBlob().getDataAsString());
var sheet = SpreadsheetApp.getActiveSpreadsheet().getActiveSheet();
sheet.clear(); // Clear existing content
sheet.getRange(1, 1, csvData.length, csvData[0].length).setValues(csvData);
}
```

Set a time-driven trigger to execute this script as often as needed.