This tutorial assumes that you already have uploaded the video to your YouTube channel and that you have a timed caption .srt file that you have received from a captioning vendor, not just a transcript of the video. If you have a transcript that you need to synchronize with your video, use the Making Captions from Transcripts tutorial instead.
Click on the drop-down list next to the Edit button for your video, and select the Subtitles & CC option.
On your video page, click the button that says Add new subtitles or CC, and select the language that your subtitles are written in from the drop down menu.
Click Upload a file in the pop up window.
Select the radio button that says Subtitles file, and click the Choose file button to find the appropriate .SRT file on your computer, then click Upload.
YouTube will then switch to a page with your video and the subtitles. If there are problems in the subtitles, you can change the text and timing of them here. Click Publish in the top right corner to finalize captions.