"Normally" does not actually exist. It's a lie. lol
If you are generally a quick learner and you are eager to learn you can get the basics down in a few months. It takes time for things to become instinct and those basic things are what you want to become instinct.
For me, I have to read books before I start messing with unfamiliar things in any discipline only because I take comfort in being introduced by professionals before I start figuring out things on my own. ( it has not always been the case but still)
Some people just like to jump in and mess around with stuff. The problem with that is that when you discover that something works you tend to use it even though there are much better ways to accomplish the same task.
Good luck learning C++. I learned it for my degree and even though I never used it outside school, I am grateful they forced it on me because being proficient in C or C++ means you can be proficient in any other high level language, trust me.
It took me a bit less than 2 weeks to learn the workings of C++...the language is easy, but I already knew Java, so there isn't too much to learn between the two. But Da0omph is right, you always learn something new.
To learn the syntax, a couple of weeks. To learn to think about problems in such a way that the solution lends itself elegantly and simply to C++, and in doing so become a good C++ programmer; potentially years.
"How long does it normally take to learn c++ basics?"
Any estimation of time is guaranteed to be inaccurate since it depends on too many personal factors; even the density of the air probably affects the rate at which you learn.
Personally, it sounds to me like your impatient to some degree. If you weren't, you wouldn't ask this question. Only time will tell.