To receive text messages on your phone, go to Settingsand Devices and enter your cell phone number. You will be asked to confirm your cell phone by sending a requested password to Twitter at their SMS phone number, 40404, on your phone using SMS or text messaging.
To receive updates as text messages, click the cell phone icon next to "Following" for each Twitter account you follow.
That's all there is to get started! For more information about Twitter, here are some helpful resources: