To create a new playlist, first click the Playlists button on the sidebar.
From this menu, you'll click Create Playlist. Simply give it a name and click the checkmark, and it'll be created.
Until published, created playlists will not be visible for anyone except you.
To add a video to a playlist, you have a few options.
When not viewing a video, click the three dot menu, select Add to Playlist, and select the playlist you'd like to add the video to.
When viewing a video, click Save button under the video and select the playlist you'd like to add the video to.