I'm constantly running into people who are unsure, afraid, overwhelmed, etc. about the move from Visual Basic 6.0 to Visual Basic .NET. The reality is that although there are a lot of differences, there are also a lot of similarities. Depending on the type of development you do, you might find that there is very little difference in how you develop today when moving to VB.NET. I'm not trying to downplay the differences, but I don't want to jump on the Visual Fred bandwagon either, as I think they are slightly exaggerating how difficult it is to move forward.
The key point being that once you get past the differences, a whole new world of possibilities becomes open to you. Things that just were not possible (or were extremely difficult and possibly unreliable) are now possible with VB.NET.
There is a ton of information that will walk you through the steps of getting from one to the other available from many sources. Here are a few.
Use the Code Adviser for Visual Basic 6.0 on your existing code prior to upgrading.
Adding Code-Checking Rules to the Code Adviser for Visual Basic 6
Dr. GUI .NET 1.1 #0 - Introduction to .NET, Hello World...
Introduction to Visual Studio .NET
Raising Events and Responding to Events
Understanding and Using Assemblies and Namespaces in .NET
Variable and Method Scope in Microsoft .NET
Upgrading VB6 to VB.NET
Upgrading from Visual Basic 6.0 (MSDN Documentation)
Calling COM Components from .NET Clients
Differences Between Visual Basic 6.0 and .NET Controls
Introduction to Exception Handling in Visual Basic .NET
Error Handling in Visual Basic .NET
Managing Versions of an Application
Replacing API Calls with .NET Framework Classes
Using ActiveX Controls with Windows Forms in Visual Studio .NET
Accessing the Registry with Visual Basic .NET
Life Without Control Arrays in Visual Basic .NET
Life Without On Error Goto Statements
Property Bag Changes in Visual Basic .NET
Developing Windows Forms in VB.NET
Getting Started with Windows Forms
Creating Classes in Visual Basic .NET
Creating Components in .NET
Creating a Windows Form User Control
Common .NET Libraries for Developers
Performing Drag-and-Drop Operations
Working with MDI Applications and Creating Menus
Moving from ADO to ADO.NET
Inheritance and Interfaces
Inheritance from a Base Class in Microsoft .NET
Understanding Method and Operator Overloading
Overloading Methods in Visual Basic .NET
Overriding Event Handlers With Visual Basic NET
Walkthroughs in Visual Basic and Visual C# (MSDN Documentation)
Asynchronous Execution in Visual Basic .NET
Creating Your Own Dynamic Properties and Preserve Property Settings in Visual Basic .NET
Deploying Hybrid Visual Basic 6.0 / Visual Basic .NET Applications
Exploring the Visual Basic .NET Resource Kit
Multithreaded Programming with Visual Basic .NET
Object-Oriented Programming in Visual Basic .NET
Overriding Event Handlers with Visual Basic .NET
Performance Optimization in Visual Basic .NET
Using Classes and Structures in Visual Basic .NET
Using GDI+ and Visual Basic .NET
Visual Basic .NET Internals
Continue reading through the Dr. GUI .NET series.
Take the online seminars available on MSDN.
And finally, don't forget about The .NET Show