Like varjak paw said, the client is only part of the ARD solution. By enable the client on your computer, you can connect to it from another mac on your local network using Apple Remote Desktop.
If your looking for a free altertive you could try VNC. The limitation of ARD and VNC is that without configuring your firewall you won't be able to connect to your mac from over the internet.
If you want an easy way to connect to your mac from over the internet I would suggest checking our logmein.
Thanks , I did download the aplication but it said I already had the application installed (newer version). Apparantly it comes with Lion as standard. So if I have it installed I am not sure where to find the dashboard widget mentioned at http://www.apple.com/remotedesktop/newfeatures.html . It does not show up when trying to add further widgets.
Again, the ARD application does not come with Lion. Did you buy the ARD application from the Mac App Store, or did you just download the client updater? If you did buy the app, it should be in the Applications folder. You need to run that at least once so that all the components get installed. Then the Remote Desktop Dashboard widget should appear.