no activeX, now what?

Okay, please forgive my ignorance, but I am still
leafing through some books trying to find the best one
to start reading.

It is my understanding that ActiveX is dead in vb.net.
So my question is: now what?

What I have is an application that needs to run on the web as well
as a stand-alone program.
What we have done in the past is to create a .dll that would take input
-from the web or a stand alone app - and return good things
in a pre-determined way.

How does one accomplish this with .net (simple explaination please)
What I need to know is what should I start looking at for an
acceptable way to do something similar.
I'm guessing webservices and XML have something to do with it?
..or am I able to do the same thing with .net, that is, code in once
place interfacing with different User interfaces?

use namespaces to order it like you would COM (this.that.dothis)and then use it on the web or on the client