Plink is a command line application. This means that you cannot just double-click on its icon to run it and instead you have to bring up a console window. With Windows 95, 98, and ME, this is called an "MS-DOS Prompt" and with Windows NT and 2000 it is called a "Command Prompt". It should be available from the Programs section of your Start Menu.
To start Plink it will need either to be on your PATH or in your current directory. To add the directory containing Plink to your PATH environment variable, type into the console window:
set PATH=C:\path\to\putty\directory;%PATH%
This will only work for the lifetime of that particular console window. To set your PATH more permanently on Windows NT, use the Environment tab of the System Control Panel. On Windows 95, 98, and ME, you will need to edit your AUTOEXEC.BAT to include a set command like the one above.