Communication or Grammatically Correct?
In general, there are two styles of writing that you will have to practice throughout your Korean learning journey. The first, and arguably the most important, is "communication oriented writing" or 구어체. That is to say, writing simply for the purpose of getting the other person to understand what you are trying to say. In this style of writing, grammar is not so important. Mistakes should be made because through these mistakes one learns how to correct them. Grammatically correct writing, 문어체, is useful as well but in very different situations. The Korean written language varies GREATLY from the spoken, and so depending on what your destination on this journey is, you may choose from the following suggestions:
Kakao Talk - For those who don't know, Kakao talk is by a landslide the most used messaging app in Korea. So, we mention it here because if you can find yourself a Korean friend, then this app will be essential for communicating with them! It can be very beneficial to practice your writing through Kakao talk because the goal is communication not perfection. This will allow you to use what you know to communicate, and through reading what they say in reply messages to you, learn the correct way to say things.
Hello Talk - This is a messaging app and is mostly for practicing your conversational written Korean (iPhone link / Android link). It's not quite as focused on grammar and written Korean, however, it could be. In the app, you can find language exchange partners through one of the features. If you find a partner who is willing to help you with your writing then that's great! But since it is a mobile app, sometimes the small screen can make editing large text annoying. So if that's kind of practice is your goal, check out the next resource below.
Lang-8 - This website is an awesome resource because it is free (with some paid plans if you like, but not needed) and it allows you to get corrections from native Koreans. What do you have to do? Just correct their English writing practice pieces in exchange! It's a win win for everybody.
Daily Diary - This is a good practice a lot of people enjoy because you can measure your progress over time. However, to truly get the benefit, you should get corrections from native speakers from time to time. Lang-8 can be a good place to do this as well.
Some useful links to Korean <-> English dictionaries:
Verb Conjugation Dictionary - This is a very useful tool if you are still getting used to conjugating verbs. Also, it can be helpful to check how irregular verbs are conjugated.
Hanja Dictionary - This one can be very useful for intermediate to advanced vocabulary learning as it will help you to create a mental network of words and their connections through similar Hanja. For more about how to use Hanja to learn Korean words, here are some videos.
Naver Dictionary - Probably the most used dictionary with a variety of different sections.
Daum Dictionary - Functionally, this is almost the same as Naver dictionary. Different people may have different preferences as to layout, structure, etc.