Text message alerts are sent automatically whenever a News post or Blog post is created. Any users who are subscribed to the applicable News category, or to the Blog in question, will receive an Alert according to their individual settings. See Subscribing to text (SMS) alerts for more details on individual users' text message subscriptions.
If you simply want to send SMS messages to your site users, the best way to do that would be ask your users to subscribe to a specific category in News Manager. Start by going to News Manager and creating a new category called something like "text messages." To do this:
Go to News Manager > Categories tab, click the green "New Category" button, and fill in the Category Name.
Make sure that the "Disable Alerts..." checkbox is unchecked.
Inform your users that they should subscribe to that News category via the "Subscriptions" link in the Account bar, and elect to receive text messages.
After that, you would simply create a new post and make sure that the "Text messages" category is selected.
This would send an SMS alert for every user who subscribed to that category. You would also be able to display those News posts on your site, or not, depending on how your site's News Pages are setup.
Note: There's no way to automatically subscribe multiple users to receive News alerts. The choice to receive text messages is deliberately left up to users, because folks can be very opinionated about whether or not they want to receive text messages (and also because some users have to pay for each text they receive, and don't want anyone to have the ability to run up their cell phone bill each month).
News Manager and Blog alerts are not meant to be a mass communication for sending text messages in bulk. There are bulk-texting services available, but they are generally specialized products that are designed specifically for that kind of communication, particularly in an emergency context. This would include services such as SimplifiedAlerts.