Before you can run any Curl application you have to install the Curl Engine. It is available as the Curl Runtime Environment (RTE) which is a browser plug-in, or as the Curl IDE which is a development environment that includes the RTE.
Both are available from Curl Inc..
After downloading just open the installation file. An installation wizard will guide you through the installation.
After the installation just goto any website that features a Curl application.
Calling an applet will start the Curl Engine and the applet will run.
Note, that Curl has a security policy which uses a privilege system. Some applets needs privileges, e.g. applets that are run from your local machine. Privileges are necessary if the applet requires access to your local file system, etc. In order to give privileges you have to enter the location of the application into the Curl Surge Control Panel, under menu item "Privileged Locations".