There are many ways to approach the daunting task of learning the 2,136 joyo (常用/regular use) kanji of the Japanese language.  The first thing to remember is that this will be a process; there’s a reason why Japanese is ranked in the third and most difficult group of languages to learn (for native English speakers) according to the US State Department, so don’t get frustrated if you aren’t making progress as fast as you had hoped.  I have tried to organize and summarize some of the most popular studying approaches to save you time once you begin your quest to learn Japanese kanji.
Secondly, no one way is necessarily better than the other.  However, there are methods that are more suitable depending on how you use (or plan to use) Japanese in your daily life.  Keep in mind your own particular study habits, and how you tend to learn the best.  These are the four most common ways to tackle learning kanji based on my own experiences studying in the US and in Japan:

1. By order of frequency
2. The textbook
3. The Japanese Way
4. The Heisig Method

Before we jump in, here are some general tips on making whichever method you choose more effective:

1. Read A LOT
   The more you are exposed to different characters in various compounds and their situational usage, the more comfortable you will feel with the characters and the language.  Japanese texts and reading passages can be found anywhere.  After acquiring a base of 100-150 characters you should be ready to comprehend some simple articles.  There are several news websites aimed at Japanese children that are great places to get articles like Asahi Kodomo and Yahoo Kids.  Try the regular Asahi site or Yomiuri for advanced readers.  Some other resources are Amazon.co.jp, your textbook (I highly recommend the Minna no Nihongo textbooks), and the library (good libraries should have a section of books in foreign languages).
2. Learn to Write the First 250 Characters
   Each character is made of radicals and various similar components.  After you learn the basic kanji and their proper stroke order you don’t need to learn how to write the rest.  The more complicated characters will be made through combinations of the basic components.  Stroke order is important to learn when you first begin, because not only will it help you when you begin to write more complicated kanji but it just looks funny if you write kanji in the incorrect order.  It would be similar to seeing someone writing an ‘S’ in English and starting from the bottom and snaking your pencil line up.  It’s good to learn how to write the basics, but beyond that you should not concern yourself too much with writing the characters unless you plan on handwriting letters in Japanese for the rest of your life.  With computers and cell phones you aren’t likely to be writing the characters much, and if you do ever need to you’ll know how to write all the basic components of each character.
3. Know the Readings
   When you learn a new kanji make sure you know ALL of the readings for that character.  This will make learning new kanji compounds in the future much easier.  Invest a little more time now and save yourself the headaches later on.

4 Ways to Study

The following is a look at four of the most popular ways to study kanji, and their pros and cons:

1. Frequency Order
   The kanji are organized based on their written frequency in Japan, meaning how often they show up in the newspaper, magazines, billboards, etc.  Why study the characters this way?  So you can recognize the most common characters of the language FIRST.  The most common 500 kanji compromise 80% of the characters appearing in texts.  You won’t know the character for string right away, (糸) which is learned in 1st grade in Japan, but you’ll know how to recognize president (大統領), government (政治), and unemployment (失業) very quickly.
   • Pros:
     Know, recognize, and understand the most common kanji used in the Japanese language.  If you plan on ever using the language for your career then this order of learning the characters would be the most relevant.  You can follow the list of kanji in their order of frequency and reference other websites or books for extra examples of usage.
   • Cons:
     Without making a conscious effort to study different character compounds it may take time to learn all the readings and the most common compounds.  This method is the most flexible, but it requires the most from the learner in terms of planning your own self-study path and methods.
2. Follow the Textbook
   If you are studying in the United States or any other English-speaking country there is a high possibility that you are learning through the Genki textbook published by the Japan Times.  This is how I first learned.  The Genki textbook’s kanji section is divided by their situational use (to an extent).  In your first lesson you will learn all the numbers, their counters, money and time characters.  The second lesson is days of the week and directions.  Later lessons primarily consist of characters of common compounds, like 運 and 動 which combine to form exercise and 宿 and 題, combining to mean homework.
   • Pros:
     You learn the characters by category or situation.  The characters reinforce the topic of the chapter that corresponds with situational dialogue in the lesson, which increases exposure when first learning the material.  When you learn the characters for classroom (教室), you also learn the ones for test (試験), and homework (宿題).  This method is suitable for those who are willing to take a slower path to learning the characters.
   • Cons:
     You don’t learn some of the most common kanji until the final few lessons or even at all when following the textbooks.  相 and 政 are two of the most common characters in Japanese, however in Genki you don’t learn the former until the final lesson, and the latter you never learn.  Also not very time-efficient.
3. The Japanese Way
   The Japanese education system has set out which kanji students will learn and in what grade they will learn them.  They begin in first grade with 80 characters, then 160 in second grade, and 200 more each year after that (meaning Japanese students learned 1040 characters by the time they finish 6th grade!).  They learn the radicals, stroke count and stroke order for every character.  In preparation for a test, students of all grades can be found writing and rewriting kanji repeatedly.  The STEP Book series that go with each grade level (here’s one for 3rd graders) are very popular with students in Japan.  They are hard to find in the U.S., but can be ordered from Amazon.co.jp and shipped internationally (you will need an Amazon.co.jp account, regardless of whether you have an Amazon.com account already because they operate as completely different companies).
   • Pros:
     It works.  Native Japanese speakers learn this way and Japan has one of the highest literacy rates in the world, in spite of their difficult language.  If you use the STEP books there are a great deal of examples and sample sentences to help you.
   • Cons:
     This is definitely not the most time-efficient way to learn.  It takes hours upon hours to write and rewrite the characters in order to memorize them and how to write them completely.  It can be quite tedious and staying motivated may become an obstacle.
4. The Heisig Method
   The Hesig Method comes from the Remembering the Kanji series created by James Heisig.  This is the most innovative and unique method to go about studying kanji.   Essentially, you invent scenes and stories connecting the kanji’s meaning with the meanings of all the radical elements used to write that kanji.  The series is divided into three books: in Book 1 you learn the meaning and how to recognize all 2,042 characters, in Book 2 you learn the readings of the kanji, and Book 3 is for reading and writing the characters.  Those who’ve used this method from start to finish swear by it, while many others who have tried it and quit.  This is not a “Learn Japanese Overnight!” shortcut.  Learning all the readings and writings in a year would be nothing less than remarkable.
   • Pros:
     This is probably the most efficient method to learning all the characters.  I’ve studied Japanese on and off for ten years and probably only know about 60% of the characters.  The creation of stories helps increase the likelihood that you will remember the characters and their meanings.  If you are serious about becoming fully literate in Japanese this is certainly the quickest, if not the best, way to go about it.
   • Cons:
     While it is efficient, it is still time-intensive.  You don’t learn the readings until you’ve can recognize all the characters, which is a serious issue for some.  Also, to help remember the characters the radicals are often used for image association, but sometimes these aren’t even real radicals, just a couple of strokes taken apart from the rest of the character.
     

So there are four of the most common ways to learn and remember Japanese kanji.  Again, there is no correct to way to study kanji, it all just depends on the individual goal of each learner.  Good luck studying!  勉強を頑張ってね！

If you have any questions or studying tips and stories please leave a comment!