In Win32, I use GetTickCount to tell how long it's been since something has happened.  For example, I might do a GetTickCount when I start something and then call it again to see how long it's been since that action started.
 
What's the normal way of doing this in C# or .Net?

That would probably work for what you're doing.
 
There's also System.Environment.TickCount which returns something closer to the Win32 GetTickCount().  It returns the number of milliseconds since the system started, up to about 25 days.
 
Here's more info on that one: http://msdn.microsoft.com/en-us/library/system.environment.tickcount.aspx .