I had few issues with godaddy.com, that’s why I postponed the plan to host my domain there and finally chose bluehost.com as I was using it from last 2 years without any hassle and Customer Support Service is awesome. I liked online chatting also 😉

Let’s start step by step to transfer domain from one registrar or one hosting provider to another
Step 1
Make sure you have access to your present account and the domain name that you wish to transfer is unlocked. If not then either go to your admin panel (cpanel usually) and under domain section you will see domain manager icon/link. Click on that and then you will see unlock domain option.

If you are not able to figure out how to unlock the domain name and how to see/change EPP(Auth) code which you would be the basic step to transfer your domain name successfully. Contact the current registrar or the hosting provider to unlock the domain and to provide EPP or authorization code.

Step 2
I assume you are done with Step 1 and your domain is unlocked and you have EPP code with you. Now make sure your whois database information is upto date and turn off the privacy domain if it’s turn on else leave it.
This step is required because your new registrar will send the mail to the email id that appears in whois database for that domain name.

Step 3
Now either you will register the domain and host too with the same client or registrar may be different from the hosting provider. But I would suggest try to host your domain from whom you registered. For example: Blue Host Inc is a hosting provider and you can register the domain name from this company too. Its registrar is FastDomain Inc. So, choose hosting provider carefully and do the needful.

This step is required to make transferring easier. Once you register and have account with a new hosting provider and your account is verified there. If you are new to that hosting provider it may take 48 hours to get verified or it may take just few hours (for me it took 6 hours approx.)

Step 4
It is highly recommended that pointing the name servers to your new hosting provider before initiating a registration transfer because transfers can take 3-10 days to complete. During this time the name servers cannot be modified. If you point the name servers to it before starting a transfer, your domain will be pointed to it (bulehost DNS in my case) during the duration of the transfer and your site will show what is on Bluehost's servers.

Go to old account (I mean the existing account i.e. old one) and point the name server to point to your newly registered web hosting DNS. In my case it was bluehost, so
I updated Bluehost nameservers as:

Step 5
Now you can login to your newly registered account’s dashboard. (For me it was bluehost cPanel) and click on the domain manager under the domain section.
Then Select the domain that you wish to transfer. (One can have as many domains linked with one account as possible). Then you will fugure out that there will be a link/icon to “Tranfer this domain to your account” (for me it showed aliencoders.org)

Read the information carefully and provide the EPP code that you got from your older account and click on continue.

Step 6
Now you will get email on the same email id that you have updated in your old account which will contain the verification code without which you will not be able to proceed.
So, if you don’t have access to the provided email address, contact the current registrar to update the WHOIS contact information. It will take hardly few minutes if everything is fine). I got within 10 minutes.
 
Step 7
I assume you got the confirmation code that I stated at step 6 and now use that code as the second verification code required by new registrar and click on continue button.
And update nameservers if required, and other option like renewal scheme, contact information, privacy option. Then agree to all terms and click on Add transfer/start transfer process.

Now your old registrar will contact you and will mail you to confirm the transfer. It would take 2-3 days to get mail from old registrar, so be patient. Then respond accordingly.
Note: These are a few points to keep in mind while transferring the domain name registration.