We were an Adobe house so I did it inside of premiere. I can't remember if it was built in or a plugin but there was two ways depending on if the shoot was scripted or ad-libbed. If it was scripted, I'd import a txt file into premiere and break it apart as needed with markers on the timeline. It was tedious but by far better than the alternative - manually typing it at each marker.

I initially tried making the markers all first but I kept running into issues with the timing. Subtitles have both a beginning and an end timestamp and I often wouldn't leave enough room to be able to actually read it.

This was over a decade ago, I'll bet it's gotten easier. I know Premiere has a transcription feature that's pretty good