Before transferring data, ensure that both MySQL and Elasticsearch are installed and running on your system. Verify that you have administrative access to both systems and that you can connect to MySQL using a client and to Elasticsearch using curl or a similar tool.

Use a MySQL client or command-line interface to extract the data you need. You can use SQL queries to select the specific data you want. For example, use a command like `SELECT * FROM your_table` to retrieve the data. Export this data to a CSV or JSON file format for easier processing. You can use the `SELECT INTO OUTFILE` statement to export directly to a CSV file.

Elasticsearch accepts data in JSON format, so you must convert your exported data into JSON if it's not already. You can write a script in a language like Python, using libraries like `csv` and `json`, to read the CSV file and transform each row into a JSON object. Ensure that the JSON structure matches the intended schema in Elasticsearch.

Before importing the data, create an index in Elasticsearch where the data will reside. Use curl to send a request to Elasticsearch: ```sh
curl -X PUT "localhost:9200/your_index_name" -H 'Content-Type: application/json' -d'
{
"settings" : {
"number_of_shards" : 1,
"number_of_replicas" : 1
},
"mappings" : {
"properties" : {
"field1" : { "type" : "text" },
"field2" : { "type" : "integer" }
}
}
}
'
```
Adjust the `properties` section to match the fields you will import.

Create a script in a language such as Python to read the JSON file and send the data to Elasticsearch. Use the Elasticsearch Bulk API for efficient data transfer. The script should format each JSON object with a preceding action line that specifies the action (e.g., index) and the target index. For instance:
```json
{ "index" : { "_index" : "your_index_name" } }
{ "field1" : "value1", "field2" : 123 }
```
Use the `requests` library in Python to POST the data to Elasticsearch.

Run the script you wrote in the previous step. Ensure the script handles potential errors, such as connection issues or data format mismatches, gracefully. Monitor the script's output for any errors or warnings, and verify that the data is being correctly indexed into Elasticsearch.

Once the data transfer is complete, verify that the data is correctly indexed by querying Elasticsearch. Use a command like:
```sh
curl -X GET "localhost:9200/your_index_name/_search?pretty=true&q=*:*"
```
Review the results to ensure all expected data is present and correctly formatted. Adjust mappings or re-import if necessary based on your findings.