1. You must probably have Administrator privileges...
2. Make sure DynamIP is installed properly (I assume that DynamIP was installed into the directory C:\Program Files\DynamIP\).
3. Verify that you have the file NTSVC.OCX in your ...\System32 directory (the DynamIP installation program should have put a copy there...).
4. Start a Command Prompt Shell and make your DynamIP installation directory the current directory (using the cd command).
5. Start DynamIP with the command line switch /S (i.e. type DynamIP /S from the Command Line Prompt) and configure DynamIP so that it's doing exactly what you want it to do once it will be running as an NT Service (note that you will not be able to interact with DynamIP when it's running as an NT Service unless you log into your NT machine). You can save your settings with File|Save Configuration (or DynamIP will write the file DynamIPS.INI automatically once you exit DynamIP).
   An alternate way of getting a configuration file is to make a copy of one of your existing configuration files (e.g. from the default file DynamIP.INI) and then rename it to DynamIPS.INI. This way you don't have to configure everything from scratch if you already have working configuration.
6. If you intend to run DynamIP as an NT service without being properly logged into your NT box, you might have to define the login/password combination(s) for the dial-up networking connections you selected in Setup|DUN/RAS. The reason being that DynamIP cannot retrieve this information from your NT settings without being properly logged in. Information on how to define login/password combinations for dial-up networking connections is available here.
7. Type DynamIPS /i and hit the <Enter> key at the command line prompt to install the DynamIP NT Service. The message box "DynamIPS installed successfully" pops up if the installation went OK.
8. Start the Service Control Manager (double-click the "Services" icon in your NT Control Panel) and verify that an entry DynamIPS was added to the list of services (after installation, the startup setting is Manual and the service is stopped - you can change this to Automatic if you want NT to start this service automatically).
9. Click on the button Start to start the DynamIP NT Service. Shortly afterwards DynamIP should start. The window text reads DynamIP_S to indicate that DynamIP is running as an NT Service.

Some basic problems and solutions regarding the DynamIP NT Service are listed in the DynamIP NT Service trouble-shooting section.