I don't have any experience with the SIM300, but I'm playing with the SIM548CZ, which has GSM/GPS combined. By the looks of it they are from the same manufacturer.
I had to go looking for a datasheet since you didn't include one - is this the module you have
The way I work it is to create a NewSoftSerial connection to the serial port on the SIM300, and send commands to it using that. Be careful to not exceed the voltages the GSM module is designed for though - it seems it might not like being fed 5V signals (see page 16) from a standard Arduino. Perhaps look at this tutorial
, or use a 3.3v Arduino board.
As far as sending an SMS, look at the AT commands datasheet
from SIMCOM, the manufacturer. Page 84-85 might be of use, keep it handy anyway.
Give this a look - SSerial2Mobile
- and this as well
Remember you need to turn on the module by pulling the power switch (PWRKEY) pin 'low' for at least 1.5 seconds.
The datasheet will literally tell you everything you need to get started on your project, it is a really good one.