How to learn the .NET Framework
Learn C instead.
No, just kidding. Have you got any experience in other programming languages and if so which one(s)? The correct approach for you will be largely dependent on that. If you have any experience with Java you should try C#. If VB try VB.Net. If Python try IronPython. If Ruby try IronRuby.
It depends on your persona. Some people like the book approach - find something like the 70-536 syllabus, and start reading. Personally, I'm more "hands on" - pick a technology (for example ASP.NET MVC) and a language (usually C# or VB) and start trying things. When you get stuck, or unsure, look here (search first), then ask ;-p
Note that the language is in many ways secondary, but people tend to get religious about it...
Start off by picking one of the .Net languages to learn. I would personally go for C# as being the mainstay of .Net development. Then just go and code something, like problems from Project Euler.
Once you've mastered the basics of the language (like the data types, language constructs and so forth) then it is an appropriate time to start learning one or more of the .Net frameworks. Here you just pick whatever you're interested in, be it WPF for desktop development, ASP.NET/ASP.NET MVC for Web development, WCF, etc.
Language first, libraries second.
Like others have said, I'd say first, pick a language of the .Net framework. After you have decided on a language, decide on what type of applications you want to develop. .Net has portals for learning each application type.
Windows Clients (WinForms or WPF) - http://windowsclient.net/
Web Clients (ASP.Net or ASP.Net MVC) - http://asp.net/
Silverlight/RIA applications - http://www.silverlight.net/
Each of those sites have specifically targeted tutorials that'll help you learn the language as well as how to apply them into the types of applications you want to develop.