Start by exporting your data from MongoDB into a format that can be easily manipulated, such as JSON or CSV. Use the `mongoexport` tool, which is included with MongoDB, to export data from a collection. For example, to export to JSON, use:
```
mongoexport --db yourDatabase --collection yourCollection --out data.json
```
This command will create a JSON file of your collection's documents.

Apache Iceberg is often used with Apache Spark for processing. Ensure you have a Spark environment set up. You can install Apache Spark on your local machine or use a cloud service that supports Spark. Download Spark and configure it by setting the `SPARK_HOME` environment variable and adding its `bin` directory to your PATH.

Download and install Apache Iceberg. You can do this by adding Iceberg dependencies to your Spark installation. Modify the `spark-defaults.conf` file to include Iceberg configuration:
```
spark.jars.packages org.apache.iceberg:iceberg-spark-runtime:1.0.0
```
Replace `1.0.0` with the latest stable version of Iceberg compatible with your Spark version.

Load the exported JSON data into Apache Spark. Use Spark's DataFrame API to read the JSON file and transform it as needed. This might include schema adjustments to fit your Iceberg table requirements:
```python
from pyspark.sql import SparkSession

spark = SparkSession.builder \
.appName("MongoDB to Iceberg") \
.getOrCreate()

df = spark.read.json("data.json")
# Perform any necessary transformations
```

Before loading data into Iceberg, define the schema for your Iceberg table. This can be done using Spark SQL. For example:
```sql
CREATE TABLE iceberg_db.your_table (
id STRING,
name STRING,
age INT
) USING iceberg
LOCATION 'hdfs://path/to/iceberg/tables/your_table'
```

Use the transformed DataFrame from Spark to write data into the Iceberg table. Ensure that the DataFrame's schema matches the Iceberg table schema:
```python
df.write.format("iceberg").mode("append").save("iceberg_db.your_table")
```
This command writes the Spark DataFrame into the specified Iceberg table.

After loading the data, verify that it has been correctly transferred by querying the Iceberg table. Use Spark SQL to perform a simple query:
```sql
SELECT FROM iceberg_db.your_table LIMIT 10
```
This will help ensure that your data is correctly loaded and accessible in Apache Iceberg.

By following these steps, you can successfully move data from MongoDB to Apache Iceberg without relying on third-party connectors or integrations.