The internet is vast and full of predators. It sounds scary and it is, but everyone knows that there is danger everywhere. It isn't isolated to the internet. However, the precautions are a bit different since you are dealing with technology and fighting against predators that are much more active in this medium.
The first step you want to take is communication. You want to know if your child is ready to go online and if they know the consequences of their actions. So ask them these questions:
1. Do you know who to talk to and who not to talk to?
2. What if someone asks for your personal information?
3. Who do you give your personal information to?
Your next step is to get some child-protection software. Some of these software are free and they do a good job. However your child will be shown ads and every parent has their own opinion about that. If you don't want your child in front of ads all the time, purchase the software. You can get them for $20 - $100 or more. I believe they also have a browsers available for free and with minimal ads. Search Google for child-safe browsers.
Let your child know about passwords and how to create them. If they can't create a good one on their own, create it for them. Let them know what a password is for and why they need to have a good one. Passwords are for protection and protection is your goal. So don't ignore this. Passwords are very important make sure your children understand.
Speaking of passwords make sure you know them all. Your child shouldn't be hiding things from you, especially on social media websites. Think Facebook.com and Youtube.com. You don't them posting sensitive information or even private information. So monitor their social media use. There are a lot of predators on social media sites, not only sexual ones but viruses and Trojans.
Downloading is also a concern. You need to tell your child to look at what they are downloading, and to ask for your permission (if they aren't old enough). Downloading even certain images can have its bad effects. So tell them what is okay to download and what is not. If they aren't certain, then have them ask you!
Child safety isn't a one-time lesson. You need to teach your child to lookout for themselves on a continuous basis - that they should take be precautions when doing things online. Not that everyone is out to get them, but there are bad people in the world.