First you have to be able to log on the remote computer using windows credentials, I suggest you to take a look at this codeproject article
Windows login
When you are logged in the remote computer :
Before using this you have to reference System.ServiceProcess and add the following using :
using System.ServiceProcess;
using System.Diagnostics;
You can now access to remote process with that, the exemple only show process name but you have a lot of properties on these items.
string remoteSystem = "RemoteSystem";
Process[] proc = System.Diagnostics.Process.GetProcesses(remoteSystem);
Console.WriteLine("Process running on "+remoteSystem+" :");
foreach (Process item in proc)
{
Console.WriteLine(item);
}
Console.ReadLine();