You will need to install a user script manager extension to install this script.
YouTubeDefaultSpeed is a user script that remembers your preferred video playback speed. Also hosted at Greasy Fork, a user script repository.
Simply select one of the playback rate buttons, injected under the profile picture on the top-right, and enjoy your sped up/down videos.
Load the raw script file located at the link above to allow Greasemonkey to automatically detect and install the script. Note: you must have Greasemonkey enabled to intercept the script. Please see Greasemonkey Manual for detailed installation steps.