When starting to learn Japanese I will always recommend learning hiragana (ひらがな) and katakana (カタカナ) straight away. Why? Because it is invaluable if you go to Japan (for reading and speaking), and most study guides will use these. They are the most basic foundation of the Japanese language. They are two of the Japanese alphabets and although there are 46 characters in each of these, it is not that difficult or scary to learn them! It can be done relatively quickly!
When I started learning Japanese I had 1 hour once a week one-on-one with a Japanese teacher, and it took me about a year to learn hiragana and katakana (while also learning basic words a sentences). I really wish that I had done them within 2-4weeks by studying by myself (which you can easily do).
The magical thing about Japanese is that it is phonetic. These alphabets revolve almost entirely around "a" "e" "u" "e" "o" sounds. This makes it so easy to learn! No only that but katakana is exactly the same sounds as hiragana. The difference is that katakana is used for foreign words like sandwich サンドイッチ "sandoichi", and hiragana is used for Japanese words like three さん "san". They both use the same "san" sound but the characters are different (さん and サン). This means you only need to learn 2 characters for each sounds, and it's easy to tell which words you use them in because one is only used for 'Japanised' foreign words.
It is easier to learn hiragana first before katakana. And most methods will teach you this way.
And there are many ways you can teach yourself these alphabets. Here are a few, but you can always search yourself on google for an option that works best for you:
- Japanese for Busy People Kana - Comes with exercises and a CD and is only £8! Teaches you basic vocab at the same time as the characters.
- Japanese Kana by Hand - Free app for android that teaches you through writing the characters.
- Kana (Hiragana and Katakana) by Tengu - Uses lessons, flashcards and quizzes along with sound bites (for pronunciation) and stroke order diagrams.
- Dr.Moku - Which is a playful visual method of learning the kanas and even kanji. Has programs for PC, Apple and Android but does costs about £0.95
- Memrise - Has a huge selection of user generated lessons for learning the kanas and Japanese in general. It's great at pacing you and helping you memorise your target lesson.
- Tae Tim's Guide to Learning Japanese - A combination of youtube videos and personal tips.
- About.com Hiragana Lessons - Step by step lessons for each different group (like all "a" "e" "u" before "ka" "ki" "ku")
- Youtube - Has so many teach yourself lessons like these.
Practice words, not just symbols. Practising words will get symbols in your head faster and will start to build up your basic vocabulary.
See the J-Talk Online Memrise Hiragana and Memrise Katakana courses here to learn the kanas through the use of basic vocabulary. With over 100 hiragana based vocab and 50 katakana based vocabulary!
Edit 16/2/14: Memrise suggestion and course added. I was looking at good memrise courses for learning hiragana and couldn't find any that I liked, that actually helped the learner USE what they were learning. So I made my own and used anime society volunteers as guinea pigs to improve the course.