Civ III is a very different game from Civ II. Best to forget you ever played Civ II. A few of the crucial differences that come immediately to mind are:
* tactics. You can - and should - have big stacks of military units - stacks of death or SoD's as they are sometimes referred to. In Civ II one loss would eliminate such a stack. Not so any more, so you can concentrate your forces better. The flip side is that Zones of Control, as you knew them in Civ II, are gone - you can move your units wherever you please.
* rush building. This is really different. You can't rush wonders the way you used to, with buying prebuilds and using caravans. You can only rush a wonder with a Great Leader, and these are rare. Also, in some governments, rushing production costs you pop points instead of money!
* workers and settlers. Instead of a single unit for settler/engineers, you have to get used to the fact that settlers can only build cities and cost you two pop points. This makes early game expansion tougher, but because of changes in other aspects of gameplay and in the AI, early expansion is more importatnt than ever!
*new concepts like culture and resources. These took me some getting used to as well.
It's a different game. It's tricky because things that seem familiar may work in a very different way (like espionage, or city walls) so you can be caught off guard if you expect them to be the same.