Transactional SMSes will typically be sent to the recipient within a matter of minutes. It may vary from 1 min to upto 30 mins.
Promotional SMSes on the other hand will take upto 3 hours to be sent.
If you have sent your SMS using the SMS API, you can check for the status of you message. Details on how to do that can be found here. If you have scheduled a SMS campaign, the status (snapshot) of the campaign can be found here .