Trading in the forex market is a high risk venture, especially for a newbie... make sure you read up on position sizing and risk management before stepping up to the plate!
Some brokers that will allow you to setup (usually 30 day) demo accounts, where you can actually trade play $...
Capital Market Services -
http://www.cms-forex.com/
Forex Capital Markets -
http://www.fxcm.com/
Advanced Currency Markets -
http://www.ac-markets.com/
Gain Capital -
http://www.gaincapital.com/
The software and services are slightly different for each, so I would recommend you do some testing of each platform and see which YOU find the most comfortable.
Also, remember that currencies basically trade around the clock [img]/images/graemlins/wink.gif[/img]