Clickatell is a popular SMS gateway, which covers 819 networks in over 220 countries.
The API offers a choice of connection options via: HTTP/S, SMPP, SMTP, FTP, XML, SOAP and COM.
To give a few examples, the HTTP method would be as simple as requesting the following URI from your application:
http://api.clickatell.com/http/sendmsg?to=NUMBER&msg=Message+Body+Here
The SMTP method would consist in sending a plain-text email to sms@messaging.clickatell.com
, with a body as in the following example:
user: xxxxx
password: xxxxx
api_id: xxxxx
to: NUMBER
text: Message Body Here
The other methods are similarly easy to interface with, in my opinion. You can check out the full details from the Clickatell API Guide.
As for message costs, Clickatell uses a credit based system. 1 credit will generally mean 1 message, but some destinations may charge a bit less (usually 0.8 of a credit) and some may charge more (usually 1.5 or 2). Apparently this depends on the network operators in the particular region. (Source)
1 credit is currently priced at USD 0.03 / EUR 0.022 / GBP 0.02. There is a minimum requirement of 400 credits, so the initial investment can be of just USD 12. (Source)
You may also want to test the gateway for free from your browser: Clickatell: Test SMS Gateway.