Facebook users without access to a mobile Facebook application or an advanced smartphone to check the Facebook site may want to sign up for Facebook's text notification system. Once you add your mobile phone to your Facebook account, you can make Facebook text you when someone sends you a message, posts on your wall, invites you to an event or comments on one of your wall posts
Procedure
1. Log in to Facebook. Click on the top "Account" link, then click on "Account Settings."
2. Click on "Mobile." Click on "Add a Phone." Type your password for verification.
3. Choose your country and phone service provider, and then click "Next."
4. Open your cell phone's messaging panel. Text the letter "F" to 32665. Wait a few minutes to receive the confirmation reply. In the reply will be a confirmation code.
5. Type the confirmation code into the Facebook mobile verification box. Now you will be directed to your mobile settings page.
6. Click on "Edit" next to "Notifications" to enable notifications by text message. Choose the types of notifications you want to receive via text.
7. Click on "Edit" next to "Text When Someone Messages Me." Choose whether to receive texts when someone sends you a Facebook message.
Note
To set a daily text limit, click on "Edit" next to "Daily Text Limit" then select your limit.
(Taken From ehow.com)