Open your Arduino IDE (see picture below). If you don't have Arduino IDE, get it here: https://www.arduino.cc/en/Main/Software. In case you are running Linux you might need extra elevation of rights (i.e. sudo su in Ubuntu) . Attach USB cable and Lilypad to your PC. Under Tools in Arduino IDE, you can check if the right Arduino/Lilypad model and port are chosen. Many times it happens your hardware seems not work. This is due to wrong hardware and port.
In Arduino IDE click File, Examples, Basics, Blink. Right after that, Save Blink somewhere else. Now, change the code. For example, reduce the blinking time from 1000 ms to 100 ms (see picture below; delay (1000). Finally, click an arrow which points to the right. It saves, compiles and sends the code over to Lilypad or Arduino. Thumbs up! Fingers crossed! If you are lucky you have your very first Lilypad app up and running!
Arduino IDE on Ubuntu Linux 14.04
Lilypad blinking internal LED