Subtitles are not available on every programme. I watch iPlayer but don't download them first, just watch them by clicking on play as they are streamed. When subtitles are available there is an s near to the symbol for making the screen large at the bottom of the play screen. Click on this to turn subtitles on or off.
On reading comments on another forum it appears that the subtitles facility is only available if you watch programmes as above or if you actually download them using the iPlayer desktop.