The biggest trick can be getting the old application cleanly off the old machine, which depends on how some plinker may have shoehorned it on there in the first place.
For simple programs created using the "Standard" subset of VB6 the Packaging and Deployment Wizard is usually adequate for creating a viable setup package to run on the target system.
This was replaced in 1998 and 1999 by Visual Studio 6.0 Installer 1.0 and then 1.1 for programmers using Professional and Enterprise editions.
There are also a number of free and for-pay 3rd party packaging products: some simple and easy, others complex, and a few that can be hazardous unless you really know what's what.
You'll be better off uninstalling the old program first in most cases.
As long as you adhere to the application development guidelines for Windows that came out while Windows 95 was still a current OS, you'll have no issues as long as you avoid anything introduced after your target OS came out. Even then in many cases Microsoft provided redist packages to add a few newer features after the fact.
However a lot of casual plinkers tended to do silly things that violate the guidelines. This is one major source of problems when moving between Win9x, older systems like XP that let you get away with pretending you are on Win9x via appcompat, and modern versions of Windows that enforce more of the development guidelines.
But a professional programmer who has kept up with things won't have many problems. It's the kasual koder who gets stuck.
