First, ensure you have the necessary environment configured. This includes having Java installed, as well as Apache Spark or Apache Flink, which are compatible with Apache Iceberg. You will also need AWS CLI configured with access to your S3 bucket.

Use Apache Iceberg's capabilities to create a new table in your desired storage system (e.g., HDFS, AWS S3, etc.). This can be done using Apache Spark or Flink. For example, in Spark, you can define a new Iceberg table using:
```scala
spark.sql("CREATE TABLE database.table_name (column1 TYPE, column2 TYPE, ...) USING iceberg LOCATION 's3://your-bucket/path/'")
```

Load your data from S3 into a Spark DataFrame. This can be done by specifying the S3 path and the data format. For example:
```scala
val df = spark.read.format("parquet").load("s3a://your-bucket/path/to/data/")
```
Ensure that your Spark environment is configured to access S3, typically by using the `s3a` scheme and setting appropriate AWS credentials.

Before writing data to the Iceberg table, you may need to perform transformations to match the schema of the Iceberg table. Use Spark DataFrame operations to perform any necessary transformations:
```scala
val transformedDf = df.selectExpr("column1 as newColumn1", "column2 as newColumn2")
```

Write the data from the Spark DataFrame into the Iceberg table. Use the DataFrame's `write` method and specify the Iceberg table:
```scala
transformedDf.write.format("iceberg").mode("append").save("database.table_name")
```
This action will move the data from the DataFrame into the Iceberg table stored in your specified location.

Once the data is written, it's important to verify that it has been correctly transferred. You can do this by querying the Iceberg table using Spark SQL:
```scala
spark.sql("SELECT * FROM database.table_name LIMIT 10").show()
```
This will allow you to inspect a sample of the data to ensure it matches your expectations.

Finally, consider optimizing the Iceberg table for performance. This includes compacting small files, removing old snapshots, and setting up partitioning if applicable. Use Iceberg's built-in capabilities to manage these tasks:
```scala
spark.sql("CALL iceberg.system.compact('database.table_name')")
```
Regular maintenance will ensure your Iceberg table performs well and remains efficient over time.