Hi There-
I'm a children's librarian in a public library and we struggle with this all the time. As another poster suggested, first look and see if your Internet provider offers any parental controls. Some of them do, some of them don't, and there is a varying degree of effectiveness for all of them.
If your provider does not offer parental controls, or if you don't like how they work, there are commercially available Internet Filters that you can purchase and install just like any other software. They have their own ups and downs. Some block sites with certain words from appearing, but a computer can't judge an image file for content, so naughty pictures with innocent file names will get through. Also, the list of words it blocks can limit legitimate searching...the famous examples are filters blocking sites about breast cancer or recipes that call for chicken breasts...you get the idea. The other kind of filter blocks actual urls. The problem with this kind is new websites are contantly popping up and it may take the company a while to discover the site and block it. Also, these companies often consider the list of sites they block to be a propriatary secret and unfortunatly, they seem to include sites that they want blocked for political reasons. I have experimented with many differnt kind of filters and have been dissapointed with all of them. I have never tested one I couldn't "get around" and I have never had one that didn't block things that really shuldn't have been blocked. That being said, for a home environment, it is easy enough for you to disable the filter if it is blocking something you want to get to, and if you are monitering your kids you will pick up on it if they are trying to get around the filter. Remember too that filters are only a tool and cannot take the place of having conversations with kids about the Internet and how to use it, since sooner or later either the filter will let something through, or your child will be at a friend's house, a library, etc. where there is no filter and they will need to know how to use the computer responsibly without one.
Personally, I like the idea of setting up a folder of bookmarks for the children's favorites sites. You can even add a kid friendly "search engine" to the list like Yahooligan or Kids Click, which don't search the whole Internet, but just a database of kid approved sites. The best and most lasting thing you can do is have frank conversations with your kids about the Internet and how to use it. Teach them to never type a web address into the address bar of a browser, but to always go through a search engine. I tell kids that the Internet is like a large city. There are wonderfuls stores, and cultural and educational resources, and fun places to hang out, but you don't just walk through any door you see. You might ask your local public library or school, they often have brochures or workbooks that help sort through what to do with kids and the Internet.
Hope some of this helps and good luck with whatever you decide to do.