1. Go to your youtube studio. (Link)

2. Select the subtitles tab on the left.

3. Select the video you wish to add subtitles to. This will take you to a new page.

4. Click on the blue 'Add Language' button, and select a language from the dropdown menu.

5. A new line will have been added to the menu. Select the blue 'Add' link under the subtitle column.

6. At the new page, select 'Upload File'.  Find the SRT file, and Publish.