YouTube is actually pretty good at resizing your video to the required size. Unless you are looking for optimal quality, try simply uploading your video and see how it turns out first. Why fix something if it isn't broken?
WordPress can natively embed videos right in the editor. Simply place the embed shortcode tags before and after the URL. If the address magically turns into a link, you will need to break the link using the unlink tool in the editors toolbar. Some editors may also have this option in the context menu.
For other websites, you will need to copy and paste the code, provided to you by YouTube, into the HTML code (not the WYSIWYG editor)
Height and Width
The height and width of a video is dependant on the resolution of the video. If you want to change the hight or width, be sure to specify the correct aspect ratio or you may find your video appears stretched horizontally or vertically.
Undesirable Screen at the End
If an undesirable screen shows up at the end of your video, append the following parameters to the URL: ?hl=en&fs=1&rel=0
Unless your CMS has a button in the editor to insert YouTube videos, you will need to insert the code into the HTML. Be aware that some editors change a single ampersand (&) to & each time you save. Obviously this can cause your code to fail. If this problem happens to you, restore multiple &amp;'s back to a a single & in the code.