You can buy domain name of yours from any domain registering company , the pricing are ranging from $5 to $10 (lees with hosting packages) per year. But if you buy from any company other than google/blogger dashboard than you need to change CNAME record in the domain name control panel.
Now how to shift to custom domain using our blogger dashboard ?
From dashboard go to settings> publishing > then click on switch to custom domain >
Now you have to choose the domain name , the extension available are .com, .org , .net, .biz, .info
Please see the picture below ( click to enlarge )

After choosing the domain name , you have to make the sign up and payment procedure.
Your custom domain name starts working within few minutes . (my experience) .
Now what are the advantages and disadvantage of shifting to custom domain ?
Benefits or advantages of shifting to custom domain
1) You get your unique identity for your blog owned by you. Makes you also feel little better.
2) You get more and better advertisers . You may get higher paying cpc or ppc ads .
3) Many advertising network programs do not allow publishers with free domain , so you get approved there.
As your old url will be there in search engines , blog directories etc. what about the traffic coming from all these sources to your old url ? There is no need to worry as blogger / blogspot gives you facility of redirecting all your traffic to new custom doamin url .
Disadvantages
Are there any ? yes
You have all you internal and external links in posts, blog directories etc. pointing to your old url ( yourname.blogspot.com) so it is better to change it to your new custom domain name (yourname.com) . Please check your blog is pointing to http://yourname.com or http://www.yourname.com and use the new url accordingly. it is important from search engine point of view.
Now think of what happens to your search engine entries and ranking and also alexa rankings ?
Awaiting your comments ....