How to read emails on mail server ?

First of all there are multiple protocols to retreive mail:
POP3, IMAP, etc...
I suggest you start by familiarizing yourself with the various components that make up an e-mail system.

• Mail Transfer Agent (Protocol: SMTP)
• Mail Delivery Agent (Protocols: POP3, IMAP)
• Mail User Agent (Outlook, Webmail, Thunderbird, your application)

Basically what you are trying to write is a Mail User Agent. A mail user agent has to "fetch" the mails from a Mail Delivery Agent using either POP or IMAP.
This means you will have to learn about these two protocols:
POP3 RFC: http://www.faqs.org/rfcs/rfc1939.html
IMAPv4 RFC: http://james.apache.org/server/rfclist/imap4/rfc2060.txt
Since e-mail communication happens using TCP/IP you will have to learn how to use the classes in the System.Net.Sockets namespace.
Also take a look at the TcpClient class.
Try to understand these concepts first and then I suggest you start out with POP3, this protocol is quite easy. If you have problems then with very specific TcpClient code please update your question or post a new question.
Hope this sets you on the right track.

P/S: I've complete my first program that read emails in Gmail & Download the attachments in selected emails (using VB.NET 2008).