ShellExecute equivalent in .NET
Process.Start.
Note that advanced uses (printing etc) require using a ProcessStartInfo and setting the Verb property.
System.Diagnostics.Process.Start(command)
I bet you had trouble finding it because it is in the System.Diagnostics namespace. "Diagnostics"? Usually with 20 years experience one thing you get good at is guessing at what something will be called in a new API/language, but this one tricked me.
Did you try System.Diagnostics.Process.Start() function... It's more or less similar to ShellExecute. You can open exes, documents. I haven't checked printing yet, Marc has told you how already.