I am an SMS newbie so
This is easy. Yes, you need a "sms gateway" provider. There are a lot out there. These companies provide APIs for you to send/receive SMS.
e.g. the German company Mobilant provides an easy API. If you want to receive a SMS just program a simple PHP / JSP / s.th.else dynamic web page and let Mobilant call it.
e.g.
You really don't want to setup your own SMS Server or Center ;-) This is really expensive, takes months to setup and costs some nice ferraris.
Use a provider and pay per SMS. It's the cheapest and fastest way.
You actually don't need an SMS gateway; nearly every cell phone can send/receive SMS messages to/from any email address. I built an SMS service (http://www.txtreg.net) using Nearly Free Speech's ability to forward email to a URL as a POST request. User sends a text to an email address, PHP script processes it, and sends an email right back to their phone.
Agreed with Kannel. You can set it up on a LAMP server with a GSM modem too.
Try SMS Enabler software. To receive SMS messages it uses a 3G/4G/GSM USB modem connected to a pc. It can forward incoming messages to a URL over HTTP, or store them in a database table, or write them to a CSV file, in real-time.
I used kannel on a linux box with an old mobile phone connected via a serial cable to the box. Got a pre-paid card in the phone as I was using it for private use only. Worked like a charm!