For Windows machines, I think there should be Japanese fonts already installed, you would just need to make sure you go into your computer's language settings and add Japanese to it.
Once you added it in, you can switch between language inputs in your taskbar:
And yes, you actually can just type letters! Clicking that A after switching to Japanese input lets you toggle between English characters and Japanese characters:
As you type, your input will automatically convert to Hiragana and if you press the space bar, a drop-down menu pops up letting you choose the Katakana characters or Kanji that matches what you typed.
Example: Here's me typing "watashi":
If the characters you want aren't showing up, just keep pressing space until you find what you need.