This is a big topic. If you want users to respond to a shortcode (like 40404), you have to register that and pay a monthly fee for it's use ($500 - $1000/mo). If you go that route, you probably want to pay a mobile aggregator like mBlox to manage the connection for you. They have an API and you can integrate that into your application.
If you don't mind using a long code (10 digit normal phone number), you can do it with a GSM modem hooked directly to your server. But that has some redundancy and reliability issues. There is free software to support this though:
http://www.kannel.org/
http://www.gnokii.org/
If you don't mind your users needing to use a keyword at the beginning of all your messages, like "BofA BAL", you can use a shared shortcode. That's a lot cheaper and there are a bunch of providers who can supply that service.
Sorry there's not too much specific here. It's a big topic. But if you google around using some of these terms, you should find more info. Or respond back with some more specific questions.
