The quick an easy way to do this is by using RouteWare.
(
www.routeware.dk). It's not free, but if you have to do any kind of
routing work with MapInfo, this is pretty good. Worth every Euro.
If you want to DIY and enjoy a "learning experience", thn you could
implement Dijkstra's Algorithm, which is a method for finding the
least-cost path through a network ("least-cost" is what you define. It
could be shortest path, fastest, most scenic, etc.
Good luck!
- Bill Thoen