Begin by setting up your AWS environment. Ensure you have an AWS account and create an IAM user with the necessary permissions to access the S3 bucket. Download the AWS CLI and configure it with your IAM user's credentials, using the command `aws configure`. This will allow you to interact with S3 from your local environment.

You will need to install the AWS SDK for your programming language of choice, such as Boto3 for Python, and the MongoDB driver. For Python, you can install these using pip:
```bash
pip install boto3 pymongo
```
Ensure your environment supports these libraries, and they are correctly installed.

Write a script to connect to your S3 bucket and retrieve the data. Using Boto3 in Python, you can create a session and use the `s3` client to download files:
```python
import boto3

s3 = boto3.client('s3')
bucket_name = 'your-bucket-name'
object_key = 'your-object-key'

s3.download_file(bucket_name, object_key, 'local-file-name')
```
This script downloads the specified object to your local environment.

Depending on the format of the data retrieved from S3, you may need to process it to make it compatible with MongoDB. For example, if the data is in CSV format, you can convert it to JSON:
```python
import csv
import json

with open('local-file-name', mode='r') as csv_file:
csv_reader = csv.DictReader(csv_file)
data = [row for row in csv_reader]
```
This converts CSV data into a list of dictionaries, which is compatible with MongoDB.

Set up a connection to your MongoDB database. Ensure MongoDB is running and accessible. Using PyMongo, establish a connection:
```python
from pymongo import MongoClient

client = MongoClient('mongodb://localhost:27017/')
db = client['your-database']
collection = db['your-collection']
```
Replace the connection string with your MongoDB server details.

With the data processed and the MongoDB connection established, insert the data into your database:
```python
collection.insert_many(data)
```
This command will insert the list of dictionaries into the specified MongoDB collection.

Verify that the data has been correctly inserted into MongoDB by querying the database:
```python
for document in collection.find():
print(document)
```
Once verified, clean up any temporary files or data used during the process to maintain a clean environment.

By following these steps, you can manually transfer data from S3 to MongoDB without relying on third-party connectors or integrations.