If the site supports the video host (ex: youtube), it normally just requires you post a link.
However, some browsers like Microsoft Edge like to rewrite pasted links with link names (titles) included which prevents the video from embedding.
To get around this, you can right-click in the textbox and click on "Paste as Plain Text" to paste only the link.
Alternatively, you can do it via hotkeys by holding down the SHIFT key in addition to CTRL when pressing the V key (CTRL-V is normally paste, SHIFT-CTRL-V is Paste as Plain Text).