YouTube Creator Studio has a convenient tool for transcribing videos.
YouTube auto-generates some timing windows according to when it thinks there's speech, which appear as blank white boxes on the timeline, and you can type text that will be displayed for that duration. If the auto-generated timing is suboptimal, it's pretty easy to adjust it on the timeline.
It supports some shortcuts to help with transcription:
Shift + left arrow: Seek back one second.
Shift + right arrow: Seek forward one second.
Shift + space: Pause or play the video.
Shift + enter: Add a new line.
Shift + down arrow: Edit next subtitle.
Shift + up arrow: Edit previous subtitle.
Enter: Add the subtitle.
After you're done transcribing, you can press Actions > Download to download the .sbv file of your captions.
If you're transcribing in the same language as the video (which doesn't seem to be the case here), you can type all the text for the video in one text box, and YouTube will automatically assign timing for it.
Of course, when you upload a video to YouTube Creator Studio, you don't have to publish it or make it visible to anyone besides yourself (and maybe Google).
See more information on adding closed captions to YouTube at https://support.google.com/youtube/answer/2734796?hl=en.
For other options, you can look through https://blog.ai-media.tv/blog/best-free-transcription-tools and http://www.crunchytricks.com/2016/05/transcription-software-for-windows.html, but those applications seem less powerful than YouTube Creator Studio.