Unfortunately there is this "mixed content blocking issue" that is not showing the embedded YouTubes in browsers other than Internet Explorer and Safari (as of 10/29/13), so they look like this:
One thing I learned over time is that when you embed the videos, it is nice to put in a title slide like the top image because, otherwise, you just see a play button in the middle of the person's face, like this:
So, I learned to put a title slide in the video and make that the custom thumbnail on YouTube so it looks like the first example.
How to Add the Title Slide:
First, to make the title slide, go into Enhancements under the video (there are probably other ways to do all of these steps):
Then on the right side, choose "Try the YouTube video editor."
When you get into the Editor, drag the video you want to add the title slide to onto the editing area and then to add the title slide choose the a on the top right.
That will bring up some formatting options. I have only used the first one on the left; plain white text on a black background. Classic, never goes out of style. Drag that to the beginning of your video.
Then click Publish and give it some time. Unfortunately, it creates a whole new video so you need to rename it and I usually remove the "created with the youtube editor" note and tag because it doesn't seem necessary. Then delete the old one once you verify the new one is good to go. (Stabilizing a video doesn't make a new one, FYI).
How to Add a Custom Thumbnail:
To have a custom thumbnail you first have to verify your account. This basically means YouTube verifies you are not a robot or something. The first time I did this, monetizing the account was required so it's nice they've relaxed this requirement. Verifying your account also lets you upload videos longer than 15 minutes. Here are instructions on how to verify your YouTube account. It just asks you for a phone number and texts or calls you with a code. Note that this is different from when YouTube prompts you to add a back up phone number.
On the Video Manager page where you see all of your videos, click Edit. If your account is verified you'll have a Custom Thumbnail button as in the screenshot below, under the three automatically created thumbnail options.
You'll then have to upload an image. I just take a screenshot of the title slide and upload that. Save it.
Note that it does take quite a while for the thumbnail to update. I read that it can take up to 48 hours. For me it's usually taken about a day.
Side note: The video in the screenshot above is one that I mentioned I took at a concert and used the Stabilize edit in YouTube to improve. I admit I'm often confused about copyright and YouTube. So, I probably did the wrong thing by just uploading my videos and seeing what happened. I clearly indicated the name of the song and the artist and in the description included where the concert was and the date; I made no claim that I owned the material. I just wanted to share it with the world (the concert was amazing!). A few days after I uploaded the video, I got a copyright notification in my video manager saying that it matched third party content. I acknowledged the notice and YouTube kept the video up but just put an ad on it. Interesting, huh?