First go on YouTube, and search for some vids. If you found a vid, click on it. Then if you're viewing a video, under the vid, you see the button "Embed", click on it.
Then you change the settings when you embed it by changing the color the borders, video's dimensions (e.x. 480 x 385), etc. After you're finished, copy the code and paste it on your profile by going to My Account > Settings > Profile Settings.