It is not necessary to “install a Japanese IME”. iPads, iPhones, and Macs come with one built in. All you have to do is enable it as an option.
On an iPad, tap on “Settings.” Select “General” Then select “Keyboard.” Select “Keyboards” Tap on “Add New Keyboard…” Add “Japanese -Kana”
When you are somewhere and want to type, if an English Keyboard is up, click on the thing that looks like a globe (with latitude and longitude lines and then it will cycle between the keyboard that you have set. The Japanese kana keyboard is a Hiragana keyboard. As you type, Kanji and katakana will be suggested.
I also suggest that you add Japanese as a language in your list of preferred languages so that if there is any ambiguity about a character, it shows you the Japanese version and not the Chinese version. To do so, go to Settings, General, Language & Region, and add 日本語. Note that is different from changing the “iPad Language” on the same screen. If you change the iPad language, all your apps will switch to Japanese (if the develop made Japanese versions of menus, text, etc.).
Also, iPads come with a built-in Japanese-to-Japanese dictionary and a Japanese-English dictionary that works without an internet connection, but it is not directly accessible through an app (and I recall for some reason Apple has very annoyingly forbidden developers from making a direct interface like there is with the Dictionary App under OS X). To enable it, go to Settings, General, Dictionary, and check the desired Japanese dictionary options. Looking up words is not done from an app. To look something up, go to the home screen and swipe down to open the search box. Type whatever you want to look up. Almost certainly, you will see some results but not the definition. To get to the definition, you have to usually scroll down in the results and usually click “Show more results”. Eventually, there will be a Dictionary section. If what you want isn’t the first thing then click “Show more” and you will see the results from all enabled dictionaries. Tapping on a result can often get you a more detailed definition.
Enabling the Japanese dictionary is also important if you want to tap long on a word on a web page so that a popup menu opens so that you can choose “Define” and get a definition right away.