Your answer indicates that you are talking about an intranet. This means that you can do certain things that you cannot generally do with an Internet application.
Are you sure that you really want to run the program on the server or do you just want to run software that resides on the server?
If you don't care, and I suspect you don't, the simplest way is to create a shortcut to the application. To do this, the folder on the server in which the application resides must be shared. Also, if the program needs to access any files, the folders in which those files reside must also be shared. The person responsible for the server almost certainly knows how to do this. If not, contact me and I will give you instructions. The program will actually execute on your machine, even though the program and all of the data files reside on the server.
Another very popular way to execute code on the server is to use PHP or ASP.NET. Programs using these technologies reside on the server. They are invoked by a browser such as Internet Explorer or Firefox (the two most popular). Some of the code gets executed on the server and some is executed on your machine (the client) by the browser.
If you want to know the quickest and easiest way to learn the basics of these languages, you should visit
www.w3schools.com. They have tutorials with examples that are clear and easy to understand.
I hope that helps,
Hoppy