I took a few books from a public library; I saw more than 600 different pictograms. What is their official total sum? I never found any way to learn them other than learning them by heart.
the answer to your question turns out to be a complex one. firstly, when we talk about characters (i.e. 'squarish East Asian writing symbols with a certain shape, sound, and meaning'—not a good definition but maybe an understandable one), one has to know
that there are (historically speaking) both 'simple' shapes (such as e.g. 馬 ma 'horse') that are really pictographs, and 'complex' shapes (such as 媽 ma 'mother', composed of 女 nü 'female' for meaning and 馬 ma 'horse' for sound);
that both the total number of 'simple' shapes and the number of compound characters is open-ended and open to contention.
in my character database i have around 75'000 Unicode codepoints that refer to unique character shapes (and thousands that are repetitions of other codepoints); as @SYK mentions, this figure is too low by the thousands. one has to clearly say that the majority of these characters are historical variants of some other character, others are obscure, dubious, or not attestable other than in dictionaries, and that not more than around 10'000 character shapes constitute the common typographic gamut of modern China, Taiwan, Japan, Jorea, Hong Kong, and Macau.
i've done a graphical analysis on these shapes and presently use a little over 1'622 'simple' shapes to describe the setup of 75'000 characters; i expect something like 100...300 shapes to be still missing from the data, so there would be in the vicinity of 2000 'elementary' shapes in the Chinese script. talking about what is actually in use in the modern world, it's more like 10'000 characters made up from about 800 basic shapes. bear in mind however that what constitutes an elementary shape in this writing system has never been standardized, so each author has their own system.
some links to books that demonstrate that you do not have to only learn characters one by one and how components can help you: