Looking up Kanji by Reading
Kanji readings fall under one of two categories: Sino-Japanese reading or on-reading (音読み), and purely Japanese reading or kun-reading (訓読み). The on-reading or onyomi of a character is derived from the original Chinese pronunciation, from when Chinese characters were used to transliterate the Japanese language. Most onyomi clearly resemble the original Chinese pronunciation, but there are exceptions due to the vast differences in the two spoken languages. The kunyomi is purely a Japanese sound associated with characters that convey their meaning. As a general rule of thumb, kunyomi is used when the kanji is a stand-alone word (such as いぬ: dog, or くち: mouth), while onyomi, more often than not is used when the kanji is part of a compound word (such as the けん in ばんけん: guard dog, or the こう in じんこう: population). As is often the case, there are exceptions. Sometimes kunyomi is used for compound words (such as かわぐち: river mouth, or むらびと: village people) and sometimes onyomi is used as a stand-alone word (as in ほん: book). But you will notice that the afore mentioned rule of thumb usually applies.
You can search based on kunyomi or onyomi above by typing either reading into the romaji input field. You can customize the search method based on an exact reading or a reading that includes your input as part of the reading (in case you can't remember the whole reading). For help in determining the romaji equivalent of the reading to the kanji you are searching for, check out the section on Hiragana and Katakana.