With Chinese there is an awesome keyboard setting on iOS where you can draw a character, so if you see one you don’t know you just draw it into a dictionary to identify it. Obviously you can just copy and paste unknown characters but I would be surprised if there were no way on an iPad to draw a Japanese character for input. Is this true? Do Japanese people have any way for inputting kanji apart from typing the pronunciation?
The same feature is part of many Japanese dictionary apps these days. I use an app called 'Midori' and it has that feature. You just draw the kanji you want to find and it will offer candidates which resemble your drawing. You can also do this online and draw the kanji with a mouse (check it out here).
If you don't have the option of using a drawing recognition tool, you can use pop-up tools such as 'rikaikun' (for Chrome here) or other versions for different browsers. When you hover the mouse over the unfamiliar kanji, a pop-up appears that gives you information which includes the readings.
Recently, advances in technology have led to the development of Optical Character Recognition (OCR) technology, allowing you to use your phone's camera to recognise kanji characters. A Google app with that feature can be seen here.
If you have no access to digital apps such as the above, you have to go with one of the older systems devised to categorise kanji. These include systems which organize kanji variously by radicals, by stroke number (if known), the SKIP method see here, and some others.