1: The Simplest: If you do not need to embed the video you can setup blogging by e-mail and then get your users to click on the 'Send this video by email' option displayed on each YouTube video.
Beware, all posts sent to your blog-by-email e-mail address will be posted!!
2: More In-depth & More Secure: If you require embeded videos. Create a PHP page on your site that frames YouTube, then reads the value of the embeded video text box on each YouTube video and then inserts the post into your blog.
There is no need for PHP code in order to embed a YouTube video. You can simply follow the tutorial below for customised code (embed on your website using HTML code)
1. Find a YouTube video (e.g. https://www.youtube.com/watch?v=sTGxOqp3qB8)
2. Click Share
3. Click Embed, tweak the options and copy the iFrame code.
4. Paste the iFrame code in the correct place of your HTML file and the video will now be embedded on your site.