Generally, you should be able to just grab the video URL and paste it in the content section of the page.
Alternatively, on Vimeo underneath the video there is a share button.
Once you click that, it brings up an embed code which you can copy & paste into the code tab of the page editor in Givecloud. In the share modal in Vimeo, at the top right of the embed code, there's a link you can click to give you more options (whether you want the video to be fixed size or responsive, whether you want it to autoplay etc).
Embedding a video from YouTube is similar, you can click the share button underneath the video and grab the link and paste it onto your page, or click 'embed' and grab the embed code and paste it into the code tab
If the video doesn't appear to be responsive to different screen sizes, there's some code that you can add:
Jump into the code tab in the page editor in Givecloud
Add the following class to the iframe
This means that the video will automatically adjust to 100% width of whichever screen it's being viewed on.