Study Books and Dictionaries

Although CLAIR provides free online learning for its correspondence course (starting in November every year) you'll probably want to start studying sooner, and have a wider range of resources. All of the recommended books listed below are available from Maruzen bookstore, next to Sendai Station. Many are also available online from Amazon or Rakuten, possibly at a discount. If you want to study before departing for Japan, check out the online selection, and definitely consider learning kana before you arrive.

Hiragana and Katakana
Learning kana (the phonetic Japanese alphabet) is probably the best place to start when studying Japanese. Being able to read kana will be a big help when using grammar textbooks, and even for every day things like reading menus. Two popular textbooks are Kana Can Be Easy and Remembering the Kana. Both feature mnemonic pictures and rhymes designed to help you remember the shapes and sounds of the kana syllabary.

Kanji

Once you've learned the kana, you can move onto kanji (Chinese characters), which are used to write the majority of Japanese words.  Again, Maruzen has a great selection, some of which are also available from Amazon. Two popular books are Remembering the Kanji and Kanji Pict-o-Graphix. As with kana textbooks, many kanji books feature mnemonics to help you master the shapes and readings of the kanji. Kanji flashcards are also good for practicing and testing your knowledge. Try Tuttle Kanji Flashcards. Many people also utilize SRS (spaced repitition systems) for memorizing the characters. Anki is a very popular one that also has smart phone application usage available. The Kanzen Master series is also quite popular amoung students studying for the Japanese Language Proficiency Test (JLPT) when it comes to studying kanji, grammar, and reading.

Grammar Textbooks

Once you can read kana, it's time to start studying the basics of Japanese grammar and vocabulary.  There are several popular textbooks recommended by ALTs. Most come in series, with the main text and accompanying workbooks, CDs, etc. Popular choices are Japanese for Busy PeopleMinna no NihongoGenki, Yookoso and Shin Nihongo. Many books are available to borrow from the library at the Sendai International Center, but it's probably best to get your own copy after deciding which series you like best.  A Dictionary of Basic Japanese Grammar (published by the Japan Times) also comes highly recommended for its clear explanations and examples of grammar usage. The Donna toki dou tsukau Nihongo Hyougen Bunkei Jiten (どんなときどう使う日本語表現文型辞典) is also quite popular among advanced learners of the language.

Dictionaries
There are several good dictionaries on the market, most popular are those published by Kodansha. Try to buy a dictionary that uses kana and kanji. A Romanized-Japanese dictionary will actually slow down your learning in the long run, and won't help you to check the kanji. When buying a kanji dictionary, make sure it features furigana (kana readings of the kanji) so that you can actually read the answers. Kodansha's Furigana Japanese Dictionary and Kodansha's Kanji Learner's Dictionary are probably the most popular dictionaries. 

Electronic Dictionaries

If you can afford it, electronic dictionaries are the most convenient option for carrying around. Be careful about which one you buy though. Most of the dictionaries on sale in electronic stores are designed for Japanese users, with little to no English explanations. Your safest option is a Canon WordTank dictionary, as they include English explanations, kanji readings, etc. The Brain series is also quite popular amoung learners. Most electronic dictionaries will have a jump function that will allow you to jump to the definition of unknown words in an entry just by clicking on them.
If you have a Nintendo DS or 3DS you can also buy language learning and dictionary software that can be used in lieu of a pricier electronic dictionary in much the same way.


Online Resources and Smart Phone Applications
As most ALTs wind up purchasing/bringing smart phones with them during their time here in the city, using smart phone applications or online resources may be the cheapest easiest option for learning the language. Many ALTs recommend Memrise, Anki, WaniKani, but there are many other options out there as well! Find what works best for you, and best of luck studying!