Hi~
Here is my very personal experience.
When I was on working holiday visa (2015), I was looking for a part-time job that could give me some free time to spend with my friends and bf, or traveling. I went on every little website as albamon or craigslist to find anything suitable. But, surprisingly, I found the perfect job on the "Non-teaching job seekers in Korea" Facebook page.
So here is my advice : become a member of all job seeking pages on social medias, it is where companies looking for foreigners will go first. I got a job in an IT company, with flexible work hours, free weekends and nicer pay than in usual foreign restaurants in Itaewon or Hongdae. I assume I was quite lucky to find this one, but you can actually see many good offers on Facebook.
Concerning the skills, I had to speak at least intermediate Korean (I was level 3 at that time) to be able to talk with the Korean staff. They also looked at my personality during the interview as they wanted someone sociable. And, last but not least, they were interested in my university history as the job was related to linguistics and required a diploma in the field.
But to give hope to people who can't speak Korean, the other part-timers who where hired after me weren't even a level 1... and the Korean staff was asking me or other Korean speakers, to be interpreter when needed.
It was a great opportunity to work in a Korean company and improve my Korean language skills. I also experienced the famous 회식 (company diner) and met various nice people. And I wasn't working the typical part-time job every foreigner has (like teaching, which is forbidden on a HW visa, or waitress in a restaurant, club or so).
Tips for jobs as the one I got : about the resume and CV, it is important to describe the old jobs or university degrees you got related to the job you want. And in Korea, a picture is still asked, but things are changing... Don't forget to precise your languages skills.
During the interview, wear something simple and clean, do not make up too much, smile and be natural. Always be respectful of your interviewer, and if you speak Korean you should know how to use -합니다 at all times. Being polite is really important, say hello, thank you for your time, If they offer water or coffee, accept politely even if you don't drink eat afterwards. I think the rest would be the same as other countries.
I think that's all I can say. If I think about something else, I will edit this post.
frgirlinseoul