Begin by ensuring your MySQL database is ready for data export. This involves identifying the tables you wish to export and ensuring that the data is in a consistent state. You may need to temporarily disable write operations or use a consistent snapshot to avoid data inconsistency during the export process.

Utilize the MySQL `SELECT INTO OUTFILE` command to export your data into CSV format. This command allows you to specify the directory and file name, as well as options for field and line terminators. For example:
```sql
SELECT INTO OUTFILE '/path/to/yourfile.csv'
FIELDS TERMINATED BY ','
ENCLOSED BY '"'
LINES TERMINATED BY '\n'
FROM your_table;
```

Once you have your CSV files, you need to move them to the Hadoop Distributed File System (HDFS), where Apache Iceberg can access them. Use the `hdfs dfs -put` command to upload the CSV files to HDFS:
```bash
hdfs dfs -put /local/path/to/yourfile.csv /hdfs/path/
```

Set up a Hive table that will serve as an interface to Apache Iceberg. You need to define the schema of the table to match the structure of your CSV data. Use Hive's DDL commands to create an Iceberg table:
```sql
CREATE TABLE iceberg_table (
column1 INT,
column2 STRING,
...
)
STORED BY 'org.apache.iceberg.mr.hive.HiveIcebergStorageHandler'
TBLPROPERTIES ('iceberg.catalog'='hive');
```

Use Hive's `LOAD DATA` command to load the CSV data into the Hive table. This step transfers the CSV data into the Iceberg table format:
```sql
LOAD DATA INPATH '/hdfs/path/to/yourfile.csv' INTO TABLE iceberg_table;
```

After loading the data, verify that the data has been accurately transferred by performing a few queries on the Iceberg table. This ensures that all data has been correctly imported and is accessible:
```sql
SELECT FROM iceberg_table LIMIT 10;
```

Finally, optimize the Iceberg table for better performance and storage efficiency. You can perform compaction and remove any redundant snapshots or files. Use Iceberg's maintenance commands to optimize the structure:
```sql
CALL iceberg_table.optimize();
```

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