Actually you can't buy domain names but you can rent them, by registering them with a domain registrar like Directnic.com for $15 per year. GoDaddy has cheaper prices but they also have a lot of complaints against them because their contract has sweeping language in it that allows them to take your domain for any reason. For a list of inexpensive domain registrars that deal honestly see: http://www.aww-faq.org/aww-links.html#Domain
If someone should decide to attack you on the internet you don't want them to be able to start up a web site in your name. Since my name is Ken Padgett I've registered domain names like http://kenpadgett.com and the hyphenated version http://ken-padgett.com. If you want to protect your family as well as yourself then you should also register all the variations on the names of your family members.
Creating web sites is easy and free if you use services like Blogger or Wordpress. There are also many hosting companies that will host a personal web site for free or for a very low monthly or yearly fee. For a list of free and inexpensive web hosts, see: http://www.aww-faq.org/aww-links.html#Hosting
In order to get your web sites indexed by Google you need to create some decent "keyword rich" content that will give the search engine "bots" something you want them to index. Keywords are words that you choose to get the search results you want. Keywords need to be repeated several times and included in headings. Write a biography of yourself and make sure to repeat your name (i.e. Ken Padgett) several times and in several different ways, like "Ken" and "Padgett" and "Kenneth Padgett." But don't give out too much information about yourself or get too personal because you don't want to help people who might at some point want to hurt you.
If you don't want to write about yourself you can create blogs based on your interests. If you like Hopi Kachina Dolls needlepoint, classic cars, or have several favorite apple pie recipes you can write about them. You can upload pictures from your vacations and write about your experiences. But be careful about which types of pictures you post. Landscapes and points of interest are always good, but you should not put pictures of yourself or your family online, because they can be copied and misused elsewhere.
Even when your web site is not about you, you should put your name on the page at least a couple of times. After all, the point of all this is to control what people see when they do a search on your name. You want your web sites to rank first in the results or at least be on the first page of results and those web sites that get listed should have information on them that is flattering to you.