While giving an introduction to the Internet, should I talk about the risks?
Yes.  You should absolutely identify the specific risks of each technology or tool that you are going to teach and discuss those risks before you assign students to use those technologies or tools.

The exact form of these warnings depends on what exactly you are introducing and the age of the students.  This is also a decision that should be made in the context of a school-wide policy on information technology.

If you're teaching TCP/IP to college freshmen, there's obviously no reason to go off on a tangent about the dangers of sexting.  If you're teaching sixth graders how to use your school's library databases, it's probably not appropriate for you to bring up many of the dangers of the internet.  So of course keep the warnings relevant and age-appropriate.

But if you're assigning students to create a class blog, you should give them instruction about not putting certain personal details on it, about dealing with spam, about creating and protecting a secure password.  If you're using a social media group (like a facebook group for the class) you should remind students about school policies that apply to the group (about swearing, offensive materials, cyber-bullying, cheating).  If you're teaching php development for a database app, you should warn students about SQL injection attacks and other common security risks. 

Keep in mind that it's unlikely that you'll encounter students who haven't already used the internet.  My son is four and he's a big fan of YouTube already.  So remember that you aren't really introducing "the internet" - you're introducing a specific tool or technology.  Your obligation is to teach the risks of that technology.