I originally learned C++ in a high school class in 11th grade. It was very very intro (we covered functions, that's just about it). I started to get into it on my own, but really came back to it in college when I started my CSC major. (Took me a lil over a semester to get everything I know now down pat.)
I think if you already know one language (preferably that uses OOP), then you shouldn't have a problem with anything else. C++ took me about 2 semesters to learn the basics... to seriously learn it and not pretend like I do. By that I mean doing OOP, several ADTS, templates, and some advanced stuff like doing outcalls to assembly within C++ code. This is just the basics. But once you're comfortable with at least one language, learning anything else is a piece of cake. Just learn new syntax, some functions, and the rest will be easy to pickup. Concepts will be the same, syntax of course will be different.
If you wanted to know how long it took me to learn my first programming language, which was QBASIC, then that could easily depend. When I started QBASIC I was about 13 and didn't care for it. So I can't really say how much. Maybe a few months. My other friend who loved programming at the time learned it in a few weeks. He did it everyday. So it depends. Just practice a lot and look at sample code is all I can say.
I started with the C language, while there are many similarities there is that OOP aspect to get down. You will be tempted to use some of the old tricks at first but you will soon over come that, once you find out there are much easier ways to do things.
Concrads on joining to OO world should take only a month or two before you are ready for linking lists and building data sructures.
Whoa, yeah, time does fly. Well, even if you still don't know C++, I'm sure you learned other stuff. I always try to keep myself active in something, even if I don't acomplish something else. For example, now I'm a better ColdFusion programmer and know more about SQL Server than I did a year ago, while I was originally planing on honing my skills more on PHP and MySQL.