What is the best way to learn Hanja (한자 漢字)?

ANSWER: By learning to read and write Chinese characters in sentences, instead of just words. But learn to read and write the traditional Chinese characters instead of the simplified characters. Why? Because Koreans use the traditional characters, not the simplified ones. That means you should probably get your reading material from places like Taiwan and Hong Kong, where they still use the traditional characters. And you do not have to learn Chinese pronunciations to learn to read Chinese sentences. You can learn to read Chinese sentences using Korean pronunciations. The goal here is to learn to read Chinese, not speak it.

If you want to learn to read Chinese sentences, you will need to learn Chinese grammar, but, fortunately, Chinese grammar is not that difficult. And since Chinese grammar is made up of Chinese characters, when you learn Chinese grammar, you are also learning Chinese characters. And by investing just a little bit of time to learn Chinese grammar, you can learn to read in another language while also learning Chinese characters and reinforcing your understanding of them, and that will help you improve your Korean language skills.

The Chinese use some characters and words that Koreans do not usually use, but it is better to know too many characters than not enough. Also learning characters that Koreans do not use will still help you increase your understanding of Chinese characters in general. 

These days Koreans do not usually write in Chinese (한문 漢文), but they used to, so if you are interested in reading Korean historical documents, you will need to learn to read Literary Chinese, which is an older form of written Chinese, a form that needed fewer characters to write. 

Written Chinese today is based on spoken Chinese, so today a Chinese person can read a book to another Chinese person, and that other Chinese person will be able to understand the story without actually seeing the writing. But written Chinese in the past was meant to be read, not spoken. It was a kind of shorthand for spoken Chinese. A person would have needed to actually see the Chinese characters to really understand the story in the written Chinese of the past. A Chinese person cannot usually just hear the sound of a character and know its meaning since many characters have the same sound, so in spoken Chinese, two- or more characters are usually used together to form words.

The Chinese character for "raven," for example, is 鴉 (아), which is made up of the sound character (牙 아) and the meaning character (鳥 조), which means "bird." so when you see the Chinese character 鴉 (아), you know it is the "bird (鳥) 아," which the Chinese know to mean "raven," not some other 아 sounding character. But what if you cannot see the character? Then you would not know which 아-sounding character it was. So, to express the meaning of "raven" or "crow" in spoken Chinese, the Chinese have added to 鴉 (아) the character 烏 (오), which means "crow," to form the 2-syllable word 烏鴉 (오아), which I think can mean either "crow" or "raven." When you say 烏鴉 (오아), it is like saying "the crow 아," giving Chinese people the clue they need to understand the word.

By the way, the character for "bird" (鳥 조) and the character for "crow" (烏 오) look very similar, so be careful not to confuse the two.

Don't worry about learning to read simplified Chinese. If you learn to read traditional Chinese, then learning to recognize simplified Chinese characters is just a matter of time. And then later, if you want to, you can learn the Chinese pronunciations to learn to "speak" Chinese. In the meantime, you can think of the Korean pronunciation of the Chinese as just another dialect of Chinese. There are many.