DLNA is built-in to the gallery app (and a other pre-loaded apps) on the HTC One. All you have to do is simply choose "Select player" from the menu (upper right corner of the screen) when viewing an event or album in the gallery app. You will then see a new windows that says "Searching for Wi-Fi players...". After a few seconds, you should see a list of all DLNA-compliant players that are available on your current Wi-Fi network. Just pick a player and press the play button to begin streaming media to the selected player.
I have had mixed results using DLNA to stream photos and movies to my LG TV and my Western Digital WD TV Live. I am still trying to determine what makes one movie file play, while another similar file will not. It is sort of hit and miss for me at the moment. My previous HTC EVO 4G LTE (and EVO 3D, for that matter) could stream media of all types to each device without any issues. I hope that there will be a system update that will make DLNA work a bit better, but I can only hope.
I hope this helps.
Also, there is a "Media Output" option in the system settings menu of the HTC One, but this option appears to be limited to the HTC Media Link HD.