I have a website written in C# and when a user does something I want to be able to send an IM message to an admin and allow the admin to respond to approve/deny the request.
I would like to use something like MSN Messenger or AIM so that the IM messages can also be sent to phones as sms.
You need to pay for the use of an SMS gateway of which there are many. Typically you buy bulk messages in advance. There are very few (if any) free gateways out there as we all know what scalping b*stards the cellular companies are. IIRC, the protocol used is SMPP.
http://en.wikipedia.org/wiki/SMS_gateway
If you weren't on a hosted site and owned your own hardware, you can plug any modern cell phone into your USB port and use the vendors software to send SMS either via a serial protocol using Hayes commands, or much more likely these days, a nice object model in java, C# or c++. Nokia have offered this for years.
I would take a look at Twilio (http://www.twilio.com/). They specialize in helping developers integrate SMS/Voice into applications.
Twilio is a web service that can be used to make and receive calls and text messages using their REST/XML API. You have to pay for the service, but it is very very to use.
For sending SMS messages out from the program, one simple approach is to use email (as long as you know the phone company of the person you're sending the message to). For example, to send a text to a telus (Canadian provider) phone, just send an email to [10 digit phone number]@msg.telus.com.
Different phone companies have different formats, you would need to find a list of these addresses for your area. Not all of them support receiving these messages without paying a fee, but some do.
Edit: Here is a list of addresses for US carriers, try the appropriate one and see if it will work for you: http://www.tech-recipes.com/rx/939/sms_email_cingular_nextel_sprint_tmobile_verizon_virgin/