How do you extract text from dynamic HTML without using 3rd party libraries? Simple, you invent your own HTML parsing library using the string parsing functions present in the .NET framework.
Seriously, doing this by yourself is a bad idea. If you're pulling dynamic HTML off the web, you have to be prepared for different closing tags, mismatched tags, missing end tags, and so forth. Unless you have a really good reason why you need to write one yourself, just use HTML Agility Pack, and let that do the hard work for you.
Also, make sure you're not succumbing to Not Invented Here Syndrome.