Although I personally recommend going straight to Visual Basic.NET if your new to VB programming, Visual Basic 6.0 is still VERY popular and even though Microsoft has killed mainstream support for VB 6, it is NOT going away any time soon.
There is a 22 Lesson Tutorial that starts at the very basics of Visual Basic programming. Teaches how to use variables, objects, functions, arrays, menu’s, file and database access and MUCH more. So if you are interested in learning VB 6, or maybe want to get a refresher, then check out the link below to get started.
The VB.NET version is similar to the 6.0 version. If your brand new to .NET then click the link below to get started as an absolute beginner point of view. The tutorial list is on the right-hand side of the page.