If you have kids with larger brains, the ability to type, and... shudder... even the ability to read, then you might want to set up a limited user account for them when you're just granting them access to use the internet for the first time on their own. There is, of course, a fine line between too many limits and too few, and that's a balance that every parent must determine on their own, as I'm sure opinions range far & wide as to what the "right" and "best" thing to do is.
If you're looking to get your child started with their own computer, or even just with their own user account on your computer, I've got some step-by-step instructions for you posted on my 'Clarify' account. Check them out here, and if you run into any confusion, please post in the comments and I'll try to clear it all up for you!
Happy surfing... There's all kinds of great stuff for your kid to learn out there... Helping them avoid some of the pitfalls will hopefully make it a great experience for both of you!