Here is my japanese keyboard of a laptop that I bought in japan.
There are only 4 special keys(circled red) to change between kanji, hiragana, katakana, wide characters and narrow characters. Notice that because of these keys the space bar button is much shorter comparing to that of english keyboards.
Also each key with a letter on it also contains a hiragana symbol, but japanese rarely use it. For the most part everybody is typing hiragana in english letters and then changing it to kanji by pressing space bar button. For example on my laptop the default input method was set to this, so if you wanted to change to writing directly in hiragana you would need to change some language settings.
So the way you input kanji on this keyboard is as follows. For example you want to input the word 都市, which means "town". In hiragana that would be とし and in english letters it is "tosi".
So first you type tosi on the keyboard by using the english letters. As the letters make syllables found in hiragana, the words will be changed into hiragana directly. So while you type t+o+s+i, what you see on the monitor will be as follows: ｔ, と, とｓ, とし.
The syllables here are : to(と)+si(し).
Once you type とし、 now it is necessary to change that into the corresponding kanji. Unfortunately there are many kanjis in japanese that correspond to とし in hiragana. So you need to somehow obtain the list of all possible kanjis that can be read as tosi, and choose the one that you need. Fortunately the computer does that for you.
Once you type とし and press space bar, computer will give you his best guess on what kanji could that be. If you see that this kanji is incorrect, you can press spacebar again, and then a list of all kanji variations corresponding to とし will appear. You can scroll the list by pressing spacebar or up or down buttons and then pressing enter key to confirm your selection, pressing corresponding numeral key, or by using mouse.
Here is how it appears:
After typing t+o+s+i: