If you are new to domain names and dont how mapping takes place between the domain and the webhost where you are hosting your website here is some information about that and also resources where you can try your hands on setting up a domain for free!.

Basics :

DNS (Domain Name Server) allow the users to use readable domain names instead of ip address to visit any website. eg : www.cool-blogger.com instead of typing 66.249.91.121 .
It will contain all the information on where a particular domain points.

CNAME or canonical name allow the users to have many aliases for a given address.
Eg : blog.example.com as an alias of www.blogservice.com which may belong to someone else.
Blogger.com allows their users to use this feature for pointing their domain to the blog they have hosted.

Have a try :

If you have never tried using a custom domain names and dont feel comfortable in spending money on your first domain name without having any knowledge of the domain settings panel and the respective settings you can Register a free co.cc domain which will also provide u settings panel where you can add DNS server address and cname,mx,A records etc.

Once u register a domain there, register for a free webhosting service like 100webspace . In the control panel u may have the option for adding domain names to your account. Add the registered co.cc domain name there. You may find the DNS server addresses there, copy the dns addresses and add them into the co.cc settings panel under DNS option. Go to your webhost, using the filemanager enter the folder with name of the domain. create a test index.html file with some content. It may take upto 48 hours for all the changes to take place so u wont find your domain ready as soon as these settings are complete. After some period of time you will see your test page up, which means the domain is working properly. Once you are familiar with all settings you will find it easy managing your bought domains.

When buying new domains, i prefer godaddy because the domains are cheap, they provides you an email with your domain and excellent services.

Google Pagerank, Age of the domain and the alexa rank are 3 significant things that u need to take care of while running ur blog. The mixture of all three can make ur blog/site a super success.

Google Pagerank :
Getting a pagerank can be sometimes a long work of patience as google accumulates the details after periodic 6 months of time. So it is better u start off as early as possible after crearting ur blog and work on building links. Link exchanging is the best way to get huge amount of backlinks. You may to pour some bucks out of your pocket to get your blog listed in different directories.
Pagerank come into picture when Selling your domain and Participating in "get paid to post" programs. Pagerank increases the value of your domain, and you can get great deals very quickly for your domain. In "get paid to post" programs, larger number of oppurtunities are available for higher pagerank domains.
Note : your blog URL with nofollow tag will not count for your backlinks. Pagerank has no relation with website traffic.

Age :
As the age of the domin increases its value also increases. It comes into picture when selling your domain.

Alexa Rank :
Alexa rank determines the traffic of your blog. This is important as these stats represent the popularity of your site. Alexa can help you when selling your domain and getting ads or sponsors for your blog.

Hope this helps :)