On Twitter, a direct message, also known as a DM, is a private tweet. If you receive a direct message, only you and the sender can see its contents. Twitter sends you an email each time you receive a DM, and you have the option to turn on text message notification, as well. Only people who you are following can send you a DM. Twitter does not offer a setting to turn off or block direct messages across the board as of March 2011, but you can block DMs from specific people by controlling individual follower relationships.
Log in to the Twitter website.
View the profile of one user you want to stop from sending you direct messages.
Hold your mouse over the green "Following" button above her updates. It will change to a red "Unfollow" button. Click it to unfollow her. This stops her from being able to send you direct messages, but also means that her updates will not appear in your timeline, where your followers' tweets appear.
Repeat for each Twitter user whose direct messages you want to block.
If you receive spam direct messages, report that user by visiting his profile page, clicking the gear icon and selecting "Report for spam." This will immediately destroy your following relationship, stop him from being able to follow you in the future and notify Twitter's spam team to investigate.
If you'd like to continue following someone but prefer not to receive blanket direct messages from them, consider asking her politely to stop.