don't assume it should be placed in a convenient place for the child. Place the computer in an area that makes monitoring easy.

2) Sit down with your child prior to allowing access to the internet... 

don't assume that they know they should never:

Give out their name to anyone. 
Give your address or phone number.
Send pictures or receive pictures. 
Give your email address to anybody. 
Meet with anybody in a public place.

Parent's should keep checking to see what kind of activities are going on.

This includes the over 1000 channels on IRC (Internet Relay Channels) 

3) Children's blocking software is a wonderful tool but...

don't assume it will block all areas where harm can come to your child.

4) Pen pals for children can be fun, as well as beneficial but.... 

don't assume because the profile of a chatter is a minor he/she is safe for your child to communicate with. Remember a profile is only as good as the poster who writes in the information.

5) Monitor your child's computer use, and length of time on-line... 

don't assume that after checking once everything is okay.

6) Your child's computer is like any other item they possess but... 

don't assume that you can't find out what they are accessing. Check their bookmarks, cache, or history. Learn to use the computer if you are going to allow them access.

7) If you suspect someone is trying to lure or harm your child... 

don't assume there is nothing you can do. Notify the local law enforcement agency in your area, and the local Customs or FBI office. It is a crime to lure children on the internet.

8) Finally, education is the biggest tool in understanding what can happen on the internet... 

don't assume that the dangers outweigh the good information that is available if we are knowledgeable enough to help our children attain it safely.