Did you know that it is possible to download subtitles for a YouTube video? There are free online apps that let you download them as text (.txt) or subtitle files, but you can also copy and paste a transcript directly from YouTube.
Steps
Method 1 of 2: Copy transcripts from YouTube

Step 1. Go to a YouTube video with subtitles
Open YouTube in a web browser and use the search bar at the top or other options to find a video with subtitles. To make sure a video has captions, start playing and then click the icon that looks like a box with "CC" at the bottom right of the window. If there are captions, you will see them appear on the screen.
Most YouTube videos have auto-generated transcripts. However, they are not always 100% accurate

Step 2. Click… below the video
It's the 3 dots icon below the video window. Click on it to display a context menu.

Step 3. Select Open the Transcription tab
This is the second option in the context menu that appears when you click the menu icon below the video. Click on it to open a transcript of the video in a window on the right.

Step 4. Click ⋮ then on Activate the time stamp (optional).
If you don't want the timestamp to appear next to each line of text, you can click the 3-dot icon at the top right of the window that contains the transcript. Click on Turn off the timestamp to turn off the timestamp.

Step 5. Open a new text document
Use any text editor of your choice to open a new, blank text document, such as Notepad, TextEdit, Word, Pages, or any other text editor.

Step 6. Highlight and copy all transcribed text
The best way to highlight text is to start at the bottom and then work your way up. Drag the slider to the right of the transcription field to the very bottom. Click and drag your cursor from the bottom to the top to highlight the entire transcript.

Step 7. Copy and paste the transcript
Right click on the highlighted text in the YouTube transcript. Select To copy then right click on the blank text document and choose To stick on.

Step 8. Save the transcript
To save the transcript, click File then Save as (Where Save on Mac). Type a name for your text file in the field next to File name and then click Save.
Method 2 of 2: Use a tool to download subtitles

Step 1. Open a YouTube video with subtitles
Go to YouTube on your web browser and then use the search bar at the top or other options to find a video with subtitles. If in doubt, click the play button and then select the icon that looks like a box with "CC" at the bottom right of the video window. Subtitles will appear on the screen if there is one.

Step 2. Copy the video address
Click on To share under the video then on To copy next to the address in the field. You can also highlight the URL in the address bar at the top of the window then right click and choose To copy.

Step 3. Open this page in your web browser
This is the web application that you can use to download YouTube video transcripts.

Step 4. Paste the URL of the video you want to extract subtitles from
To paste the video address, right click on the field Enter any URL to extract the subtitles then select To stick on.

Step 5. Click Extract and Download
It's the purple button on the right of the window. Click on it to extract the subtitle files from the video.

Step 6. Scroll down the window and click on SRT Where TXT.
If you want a subtitle file in SRT (.srt) format, click SRT to download the file to the Downloads folder on your computer. If you want to download the subtitles in text format, click on .txt. These 2 formats can be viewed and edited using a text editor such as Notepad, TextEdit or Word.