The Internet and search engines, combined with their ease of access and use in the modern world, have made finding most anything very easy. However, this also makes personal information more widely available--even if you don't want it to be. There are three different ways you can go about removing your information from the Internet, though usually it will never be completely wiped once it's there.
Use an online removal tool from specific search engines or locations that may have your information. For example, Google has the PhoneBook Name Removal tool to wipe all of your data from Google searches, and even prevent information from being indexed again. Other search engines have similar features that you can use yourself.
Search for websites that currently display your information and ask them to remove it. If you remove data from search engines, it may not show up from a search, but it will still be out there. Some sites have directories of common places your information may show up and give instructions on how to remove items. Since each site is different, it is worthwhile to explore. See Resources for one such list.
Use a paid service to remove your information, and keep it removed. You can hire a company, like Reputation Defender (see Resources), to remove all your information from the Internet to the best of its ability and, in some cases, continuously monitor and remove any information that might later turn up. These services usually cost money and if you opt for continuous monitoring, you may pay a monthly fee.