hi chintan,
to run your own union server you'll need a host that lets you run java applications as a background process, and allows you to run applications that bind to a port (in the optimal configuration, port 80). as paala noted, most webhosts do not permit either of those things. for basic experimentation, you can connect your clients to our public test server at tryunion.com on port 80. for a low-cost host that permits union server operation, consider
www.unioncloud.io or a pay-per-use cloud server such as amazon's ec2:
http://aws.amazon.com/ec2/lightweight vps machines are inexpensive as well. for example, serverpronto has a $12/month option:
http://www.serverpronto.com/virtual-private-server.phpor, if you're willing to set up your home firewall safely and run a machine 24x7 out of your house, you might also consider hosting your union server over your home internet connection.
hope that helps,
colin