With a Plugin
You could install a plugin, like Viper’s Video Quicktags, to embed videos. Using a plugin, you’ll only need to copy the URL of the video.
For Vimeo, that will look like http://vimeo.com/8484858585 – for youtube, http://www.youtube.com/watch?v=AvBjKeu7Aj.
The plugin will allow you to paste the URL into a wizard, which will wrap it in a shortcode, framing in the appropriate iframe call.
Or, you could embed manually.
Navigate to the Vimeo Video that you want to embed. When you hover over the video, the “Share” icon will become visible.
When you’ve clicked the share icon, a popup will open, and you will be able to select the Embed code.
You may style the embed window by clicking “Show Options” at the top right, if you wish.
Once you’ve copied the embed code, navigate to the WordPress page or post where you would like to place the video, and past the code. You must paste the code into the “text” editor. Switch to the text editor using the tab on the upper right hand corner of your post editor.
Now, click back over to the Visual (HTML) editor. You should see a large placeholder for the video.
If there is no placeholder, or you preview your page/post and there is not video, try copying the embed code again.