I'm going to start working on some C++ tutorials, but I want to start with this basic question, first.
1) You will need some books. How advanced you can start depends a lot on your background, so we'll start with that. If you've never used an object-oriented programming language before, you will want to begin with a gentler introduction. The Teach Yourself series or For Dummies books aren't bad for this, but they will not make you an expert, either. One of the best books to arrive at is The C++ Programming Language, by Bjarne Stroustrup. It is not for the faint of heart, but it will help you a LOT.
2) If you know C or Java already, be prepared for some surprises and bumps along the way. Java handles a number of things quite differently from C++, even though they look similar. Java also does a number of things for you (garbage collection) that C++ simply does not do. Similarly, if you know C, you will be tempted to do things in C++ the same way you did them in C because you can. Don't do it! C++ has its own way of doing things. If you have a C++ book that wants to teach you C first, get rid of it! C++ is not just C with classes. C++ is a different language with different rules and restrictions, as well as different preferred ways of doing things.
3) Be aware that a lot of people/companies have provided a lot of extensions to C++. For example, C++ does not provide any graphical utilities. Microsoft's Visual C++ offers additional stuff for that. Borland's C++ has different ways to do the same. wxWidgets, GTK+, and other group efforts provide more. I know that making programs "pretty" with a nice GUI is fun, but worry about how the language works, first. It is easy to get lost in exploring how various GUI toolkits work and forget how the basics work. I recommend using
Dev-C++ as an initial development environment because it's free, and doesn't distract you with lots of extras.
4) Finally, write a lot of code with patience. C++ is a language that can easily take years to become good at, and even the creator is learning new ways of using it.