Gmail Recently introduced POP e-mail fetching service right from your g-mail account. You'll be able to read email from up to 5 additional accounts, all in one place, and take advantage of all of Gmail's great features. Note that the email accounts you would like to fetch will need to support POP access.

Note: Some free email services don't support POP access at this time and This feature is currently only enabled for a limited number of users.

How to know whether you have this service available for you?

Click Settings from the top of any Gmail page.
Click Accounts.

Look for Get mail from other accounts.

Now Select "Add Another Mail Account" 

Now move to Next Step

Add your POP3 Mail Account details, and other options like Labeling your messages and whether you want to leave your mail on the other server. 

After Click "Add Account" You'll reach here

You can configure Gmail to use your own address to send mails like yourname@yourdomain.com

Which E-mail you want to use for sending you can add it here

Sending verification mail, this is to prevent some people to use gmail as a spam engine

Once you have the verification mail, get the code from the mail and put it here and verify. Done

This is your external e-mail account at your accounts page of gmail.

Lets see how it looks like when you get a mail from another mail account

Whoa, ok now you need to see how you can send an e-mail using your own mail address

It's a very good practice to labeling your 3rd party E-mails so that you can find them with a single click.

I hope you find this article useful.