Q:

Connecting a Lilypad to a WiFi network? 

I would like to connect my Lilypad Arduino to a WiFi 802.11 network that provides internet.  What is the best way of achieving this?  Can I use a XBee module and somehow interface with my home router?  Is there a WiFi option available? 
Thanks so much all! 

A:

You can buy WiFi modules with a serial interface, but they're a little pricy.  Basically you control them via UART, and you send them AT commands similar to how you controlled dial-up modems in the olden days. 

A:

Expanding a bit more. 
Davr suggested what I was going to suggest also.  Roving Networks also makes a good set of BT modules. 
To Expand.  ZigBee is a separate protocol completely from Wi-Fi.  ZigBee is similar to BT in radiated power, which relates a large amount to range, but is different in that it is designed to allow multiple nodes to create a network, each node effectively expanding the network out by it's range.  I hope this clears up that they are similar but not related. 

A:

Just wanted to share my current solution with you all:
After chatting with Marcus and Madeleine at LittleBirdElectronics, we have come up with the following possible solution:
1) Xbee on The lilypad,
2) USB Arduino, Ethernet Sheild and Xbee combo to transfer messages to the WWW. 
This is just one of many possible solutions, but for me this seems to provide the benefits of the low power and size requirements on the lilypad end by using the xbee instead of using 802.11 directly on the lilypad. 
Besides, I already had a spare Arduino and Ethernet shield going unused, and wanted an excuse to play with xbee anyway! ;-) 
Thanks all for your input!  It was very useful in devising a solution.