I need to translate a GIS program that is currently in VB6 into VFP8 that runs ESRI's ArcMap program through automation.

If the ArcMap program can be used as an automation server, you create an instance of it using syntax like this:

oArcMap = CREATEOBJECT( '< whatever the name of the application class is >' )

in much the same way that, if you wanted to automate Word, you would create an instance like this:

oWord = CREATEOBJECT( 'Word.Applicaiton' )

c:\arcgis\arcexe82\Bin\esricore.olb.

You can open this file in the Object Broswer to discover what properties you need to set and how to call its methods after you have instantiated it.