Checking mail requires accessing a mailbox, which are found near the bankers in most towns.
If you have unread mail, you will receive an icon in the right hand corner of your in-game taskbar!
When you open the mailbox, you can view your Inbox and Outbox, which can both hold 30 messages. As a tip, only 10 mail can be sent to one player at a time, so if you have more than 10 items to mail, you'll need to wait for them to receive the first 10 items before sending more.
Lastly, to send mail, click the "Send mail" button in the bottom left corner of the Mailbox menu. This will bring up the "Send mail" menu. Input the Recipient, a Pending Outgoing Message, and insert an Item if you'd like! Certain items will have a Fee to send out the mail.
You can also check the "Request" box and input a gold amount for the item you're sending. When the recipient receives the mail, they will have to pay the gold amount before retrieving the item. This is helpful if you're wanting to sell an item to another player through the mailbox.