Use Video module to insert a video from the WordPress Media Library, or use an embed code provided by a third party such as Vimeo or YouTube. Video module does a great job of being responsive on smaller devices.
If you select a video from your Media Library, you can use MP4 or WebM formats, and you can select an image from your Media Library to serve as the "poster" for the video before it starts to play. You can also set some playback options.
If you embed a video, go to the site hosting of the video and get an embed code. You usually have some options for configuring the embed code before you copy it, so there are no other general options in the Video module.
As for all modules, on the Advanced tab, you can change the margins, animate the module as it comes into view in the browser window, and control which devices it is displayed on.