Easy: go to hanjabuddy.com
Hanja refers to Chinese characters as used in Korea. There is a large shared vocabulary between Korean, Japanese and Chinese made out of these characters and in Korean they are now largely hidden.
Decades ago you would see this sort of title in Korean newspapers:
改正사립學校法 문제 많다 (= Revised private school law has many problems)
In a modern newspaper none of these would be hanja, except maybe 法 (law) if the newspaper felt like making the title more impactful - this is one of the few areas where you still see hanja in newspapers. So it would show up like this: 개정사립학교법 문제 많다
There are actually more hanja hidden inside there though, and if you were to hanjafy each and every 'hanjaficable' word it would look like this:
改正私立學校法 問題 많다
Hanja in Korean is a bit similar to Greco-Latin words in English. The more academic and formal the setting, the more likely you are to see more of them. The less formal the setting, the fewer of them you'll see. Let's take a random tweet from the singer 이적 that showed up a moment ago as an example. The tweet is about how nice it was to go on JTBC's 유명가수전 with his peers in the music industry and sing and have a drink or two.
음악하는 동료들과 모여앉아서 두런두런 얘기하다 노래하다 한잔하다 하는 시간을 참 좋아하는데 딱 그 분위기여서 편하고 즐거웠어요.
What would this look like as hanjafied as possible? It becomes this:
音樂하는 同僚들과 모여앉아서 두런두런 얘기하다 노래하다 한盞하다 하는 時間을 참 좋아하는데 딱 그 雰圍氣여서 便하고 즐거웠어요.
In comparison to the nearly 100% hanja newspaper title above, here we're already down to 11 out of 56 characters. That's pretty much the ratio of hanja in everyday Korean: I'd say about 10% to 25%.
Next up:
No. It's something that (obviously) wouldn't exist if not for Chinese, and owes its existence to that. But using hanja in Korean (and kanji in Japanese) has nothing to do with China. It's actually a bit similar to the countries Canada, Australia and the UK. These countries wouldn't exist in their current form if not for the British Empire, but on the other hand they don't operate with any concern with what the UK Prime Minister may think about this or that policy being discussed at the moment. There's a certain amount of influence back and forth between them all, but it's a sharing between equals and is in no way obligatory.
If you are a Korean and are talking about a term like the Japanese manga (漫画) or bōsōzoku (漫畵), you have two choices of pronunciation: simply pronouncing it as is in Japanese, or using the Korean pronunciation of the same characters: manhwa (만화, 漫畵) and pokjujok (폭주족, 暴走族). You can imagine that using the Korean pronunciation carries little to no Japanese connotation: the word manhwa has nothing to do with Japanese comics in Korea, despite its origin. In the same way, talking about film noir in English has nothing to do with France, but if you pronounce it as French as possible then it might.
Another reason for hanja not being Chinese (or Japanese): the three countries each use their own system now. Japanese uses a somewhat simplified form, China a much more drastically simplified one (and even tried to simplify it further, thank all that's holy that it never happened). Korea, Taiwan and Hong Kong are some of the only places that still use the traditional hanja, and in Korea of course they have largely gone out of use so that pretty much leaves Taiwan as the largest bastion of hanja as written in Korea. (Note: Korean does have a few of its own hanja that are used nowhere else, but these are pretty rare and in small number.)
Put simply, as a non-Korean (assuming you are), hanja give you an insight into the vocabulary that otherwise takes decades of use. Knowing a few hundred of them is a sort of shortcut to this. It works largely in the same way that knowing etymology of English words gives you insight into how they work:
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audio: from the Latin audio (I hear). Related words: audible, auditory, inaudible.
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-ium: a place where something happens. Auditory -> auditorium (a place where listening happens).
Now we're getting some real insight into vocab instead of just learning them as separate fragments. What other -iums are there? Well, there's planetarium, and aquarium. Ah, and there's aqua in aquarium. You'll see that in words like aquatic and aquamarine. What's that marine about? It's from the Latin mare (sea), and -ine makes it into an adjective. Wait, haven't we seen -ine elsewhere too? That's right: saline (from sal, salt), masculine, feminine, lots of places. Even the word vaccine makes an appearance here, which comes from Latin vacca for cow. The cowpox virus was originally used in vaccines against smallpox, and the name stuck. There's no end to the words we can learn this way.
That's sort of the role hanja can play for you as a non-Korean, especially if you feel like you're always just proficient, never completely fluent, and lacking something that you're not sure how to get.
With this hanja evangelizing done, why Hanja Buddy?
Typying kanji in Japanese is a breeze, and naturally typing Chinese in Chinese is a breeze as well (it's the only characters they use, after all). Let's write something in the three languages:
Japanese: かんこくごべんきょうしたいね. ("I'd love to learn Korean.") Now hit the spacebar: 韓国語勉強したいね. All the kanji are filled in and you're done.
Chinese: ranhoutashuo: ("Then he said...") The moment we hit the : key it's already turned into Chinese: 然后他说. That was fast too! Actually maybe a bit too fast if you intended to write "Then she said". But as you type you can see it as another possibility below: 然后她说, and all you have to do is hit the number 2 key and it chooses that instead.
Okay, let's type some hanja in Korean using the 한자 key on the keyboard. Oh boy. Let's use 이적's tweet again.
음악하는 동료들과 모여앉아서 두런두런 얘기하다 노래하다 한잔하다 하는 시간을 참 좋아하는데 딱 그 분위기여서 편하고 즐거웠어요.
Okay, 음악 has hanja. Let's select it and hit the key. Nothing. (Note: in WordPad and certain apps it will bring up 音樂 but here on Chrome we get nothing) Let's select just one then: 음. Hit the hanja key: nothing. We're going to have to type it out again. Type 음 and then hit the hanja key. Six results. We use the arrow keys to move down and select one. Thankfully 音 is on top, so we select it. Now we have:
音악하는 동료들과 모여앉아서 두런두런 얘기하다 노래하다 한잔하다 하는 시간을 참 좋아하는데 딱 그 분위기여서 편하고 즐거웠어요.
Time for 악! It's 樂, the sixth result. So we type 악, then hit the down arrow key five times, hit enter and we're done! Now we have:
音樂하는 동료들과 모여앉아서 두런두런 얘기하다 노래하다 한잔하다 하는 시간을 참 좋아하는데 딱 그 분위기여서 편하고 즐거웠어요.
We then proceed to finish the rest of them.
Type 동, hit the key. 同 is the fourth result so down key three times, enter.
Type 료, hit the key. 僚 is the third result.
Type 잔, hit the key. 盞 is the second result.
Type 시, hit the key. 時 is the first result.
Type 간, hit the key. 間 is the first result.
Four hanja left!
Type 분, hit the key. Scroll, scroll...nothing in the first nine results. Keep going down to the next screen...there it is! 雰, the eleventh result.
Type 위, hit the key. There it is: 圍 is the seventh result.
Type 기, hit the key. 氣 is the third result.
Finally comes 편. It's 便, the second result.
So let's count the keystrokes to turn this into hanja/kanji/hanzi.
Japanese: one (the spacebar)
Chinese: zero (one if you wanted to write 'she')
Korean:
First the hangul we had to retype: 음3 악3 동3 료2 잔3 시2 간3 분3 위3 기2 편3
Then the hanja key, down key, and enter: 음2 악7 동4 료3 잔3 시2 간2 분1 위8 기4 편3
So that's like...67 keystrokes or something. Plus all the time it takes to search through the list of hanja to find the right one. Is there any wonder Koreans find hanja a pain?
Now let's put this into Hanja Buddy and see how long it takes.
음악하는 동료들과 모여앉아서 두런두런 얘기하다 노래하다 한잔하다 하는 시간을 참 좋아하는데 딱 그 분위기여서 편하고 즐거웠어요.
Turning this into hanja is as follows:
Move the cursor to the front, and there's 音樂 already. One click.
Move the cursor to / click on 동료, there's 同僚. Click.
Click on 잔, click on 盞.
Click on 시간, click on 時間.
Click on 분위기, there's 雰圍氣 in the results. Click.
Finally click on 편, click on 便.
All done! Six clicks instead of 67 keystrokes.
The newest feature on Hanja Mode is study mode. Click on the Study button and you'll see a bunch of levels, which correspond to the Hanja Proficiency Test. Clicking on one of those will show you a random hanja meaning, and your job is to try to remember it from memory. For example if you click on 8급 (the easiest level) and get 사람 인, you'll want to try to write 人 from memory. If you don't know what it is, you can move the cursor in front of 인 to see the list of hanja and look through there, or just click on the answer key which will change it to 사람 인: 人.
Which levels would I recommend? As a minimum, if you are interested in knowing all the hanja that (nearly all) Koreans are able to read, learn levels 8 to 6. You can see them all here. You can ignore the : after some of the pronunciations: this refers to vowel length which IMO shouldn't even be mentioned in teaching hanja anymore as it has mostly been lost except by the uber correct: academics, voice actors, reporters, etc. (Ever had a teacher correct your pronunciation of what as wat by saying Don't you mean hwat? It's similar to that) Personally I think even mentioning vowel length in tests does nothing but put up barriers to learning them.
Hanja Buddy is written in Rust using egui, which is a new gui that is still in heavy development. One of the features left to fix is input on iOS. There are some other oddities with input and suffice to say it works best if you are on a PC and paste the text in. It's blazing fast, but still a bit rough around the edges. I've already found it useful for my own purposes though and resort to it quite a bit.