First, make sure your email client (Gmail web page if you’re not using POP, which if you don’t know what it is, then you’re not using it and therefore don’t need to care) sends HTML mail instead of plain-text. Gmail does this by default so you’re probably ok.
Next, if you’re embedding a Youtube video, click on the Share tab on the video’s page, click on Embed underneath it, copy the code that appears underneath (already highlighted) and paste it into your email. If the recipient of your email is viewing the mail on a browser, then the embed should Just Work.
If you’re embedding a video from elsewhere than Youtube you’ll need to follow their instructions for embedding. If it’s your own video you can’t easily embed it (I know this might seem insultingly obvious, and I’m sorry if it is- but I have no idea how much you know about this stuff!) but you can try to upload it somewhere (like Youtube for example) and embed from there. If you have your own server you can install a Web server and some media management software like MediaGoblin and host it that way.
Good luck, and I hope this helps.