Note 1: For adding a video into a SharePoint site using the default SharePoint tools, you need to have an E plan.
Note 2: To view a video you need to have Silverlight installed.
Note 3: The video must be uploaded in SharePoint.
How to do it?
Go to Site Actions – Site Settings;
In the Site Collection Administration menu go to Site Collection Features;
enable SharePoint Server Publishing Infrastructure feature.
After enabling this feature in the Editing Tools tab – Insert – Media a new command appears: Video and Audio.
If you click on Video and Audio in the active area a video player will be inserted.
This player can then be customized as needed (width, height, name, etc.).
By default you will have three option for inserting a video:
If you choose to insert a video from SharePoint or Address, that video must be uploaded into a SharePoint library, or on a video sharing website (for Address option).
The final result is: