To begin, you need to have access to the Toggl API, which will allow you to programmatically retrieve data. Log in to your Toggl account, navigate to your profile settings, and find your API token. This token will be used to authenticate your requests to Toggl's API.

Make sure you have Python installed on your machine as it's a versatile tool for making HTTP requests and processing data. Also, ensure you have the `boto3` library installed, which will allow you to interact with AWS services. You can install it using pip with the command `pip install boto3`.

Use Python to make HTTP requests to the Toggl API to fetch the data you need. You can use the `requests` library to perform GET requests. For example:
```python
import requests
api_token = 'your_toggl_api_token'
response = requests.get('https://api.track.toggl.com/api/v8/time_entries', auth=(api_token, 'api_token'))
data = response.json()
```
This will fetch your time entries in JSON format.

Once you've retrieved the data, process it into a format suitable for storage (e.g., CSV or JSON). You can use Python's `csv` module or simply store the JSON data directly. For example:
```python
import json
file_name = 'toggl_data.json'
with open(file_name, 'w') as file:
json.dump(data, file)
```

Ensure you have an AWS account and have created an S3 bucket where you will store your Toggl data. Note down the bucket name and region, as these will be required in the next steps.

Set up your AWS CLI with your access key and secret key. Run `aws configure` in your terminal and enter your AWS access key, secret key, region, and output format. This will allow `boto3` to authenticate your requests to AWS services.

Use the `boto3` library to upload your data file to the S3 bucket. Here is a sample Python script to do that:
```python
import boto3
s3 = boto3.client('s3')
bucket_name = 'your_bucket_name'
s3.upload_file(file_name, bucket_name, file_name)
```
This script uploads the file to your specified S3 bucket. Ensure that the file name and bucket name match those used in the script.

By following these steps, you can effectively move data from Toggl to Amazon S3 without relying on any third-party connectors or integrations.