The Japanese language uses at least three alphabets. The foreign words are usually written using katakana, the hiragana alphabet is used for native Japanese words and in order to make the writing more readable and more precise Chinese characters ( kanji, 漢字 ) are used.
The first two alphabets (katakana and hiragana) consists of less then 50 characters, so you can master them in a couple of days, however the kanjis need more time. If you want to pass the most difficult exam (JLPT 1 ), you need to know all of the "jouyou kanji" （常用漢字, frequently used）. This list contains 2136 characters in 2015.
The 20 most frequent kanjis
This list has been establish from the characters that are used in every day Japanese texts. Which is true in a way, but this does not necessarily mean that you will be able to read any text. There is a good news however, namely that official texts, such as contracts or instructions can only be written using these kanjis. My personal experience is that the first couple of hundreds are difficult to master, but as long as you are familiar with the radicals, you will find some kind of logic in them and the learning process will gain speed.
I could say that to reach a good „japanese-text-reading“ level, you need to study everyday for months, maybe years. And more importantly you will need to review a lot. I have collected the 20 most frequent characters for you. Previously I have obtained some articles from yahoo.co.jp and asahi.com, made a software and run a couple of analysis. I found 1361 unique kanjis in 50 articles, which is less then the "jouyou kanji", but the study is not yet complete. Here is the list: