Let your Arduino tweet without an Ethernet shield
Although using an Ethernet shield with your Arduino to send tweets is convenient and allows autonomous tweeting without a host PC, to save money Iain Foulds has described a method for an Arduino to send tweets by instead using an Internet-connected PC. To do this, a simple Python program is run on the host PC - which tweets any text received from a USB-connected Arduino board.
If this sort of project interests you, and you are wanting to create more complex Arduino-based prototypes, consider reading
"Arduino Cookbook" by Michael Margolis:
For the user who has moved from the beginner stage, the recipes in this book provide solutions for most common problems and questions Arduino users have, including everything from programming fundamentals to working with sensors, motors, lights, and sound, or communicating over wired and wireless networks. You'll find the examples and advice you need to begin, expand, and enhance your projects right away.