Some people have made javascript-based ML models to run in the browser (I think some were made for this course[1]), but these are for educational purposes rather than actual use.
Basically you get your source speech as an uncompressed WAV file, create an IBM Bluemix account (free trial), create a Watson "app" on the site (basically gives you some credentials for calling the API), and then write a script to upload your WAV file to the API and decode the JSON response.
It gets more complex when you want to start parallelizing the process to make it faster, and dealing with the results in an intelligent manner, but the initial proof of concept is remarkably easy.
If I recall, the Google one was even easier - no script at all, did it all with curl I think.