To carbon copy a letter today, simply note cc: below the final signature line with a list of other letter recipients, then print out multiple copies of the letter and send a copy to each listed recipient. For a blind carbon copy, do not list the additional recipients.
When computers were not commonly used in business offices, carbon copies were a typical method for ensuring multiple recipients received the same letter. Two sheets of letterhead with a carbon transfer paper between them were loaded into a typewriter. The impact of the typewriter's keys on the front sheet would transfer the same imprint to the second page as the first. The result was two copies of the same letter, one for the addressed recipient and one for an additional named person or to retain on file.
Today, the archaic "carbon copy" is still used to note that a business letter is going to multiple recipients by noting "cc:" at the bottom of the letter followed by the list of non-addressed recipients. Often the meaning of the "cc" today is said to be "courtesy copy," but this is a later interpretation.
In some cases, the sender may not want the addressed recipient to be aware the letter is being sent to multiple other people. In that case, the original letter should have nothing at the bottom, but the copies should be noted "bcc" for "blind carbon copy" at the bottom, with or without a list of recipients.