You would have to apply for a visit visa for UK, since you want to visit your cousin. You can apply at the British mission overseas and get all the details from there. You would need to submit your employment details in South Korea, your recent bank statement. Since you will be visiting your cousin, you would need a letter from your cousin that will explain the purpose of your visit and your relationship to him. Also if he is supporting you through your visit, you will need a proof that he has enough money to support you.