첫-, as a prefix or a modifier meaning "first" or "beginning," is useful, as shown in these examples:

• 첫 번째: 유리가 첫 번째예요. 
  => Youlee is in first place.
  

• 첫날: 학교에 가는 첫날에 늦었어요.
  => On the first day of school, I was late.
  

• 첫눈: 첫눈이 일찍 내리면 좋겠다. 
  => I wish that the first snow would come early.
  

• 첫사랑: 톰이 나의 첫 사랑이었다.
  => Tom was my first love.
  

• 첫째: 첫째, 책을 많이 보세요.
  => First, please read many books.

This colloquial connective indicates the completion of an action or event that is followed by another action or event. Its meaning is close to -ㄴ/은 후에.

• 저녁을 먹고 나서 신문을 읽어요.
  => After eating dinner, I read newspapers.
  
• 읽고 나서 숙제를 해요.
  => After reading, I do my homework.
  
• 숙제를 다 하고 나서 친구에게 전화를 걸어요.
  => After doing all the homework, I call my friend on the phone.

-거나 indicates two or more events or actions. -(이)나 indicates two or more alternative items.

(a) 

• 열두 시에 학생들이 밥을 먹거나 친구들과 이야기를 하고 있었다. 
  => At noon, students were either eating or talking with friends. 
  
• 주말에는 친구를 만나거나 영화를 볼 거예요. 
  => I'll either get together with my friend or go to the movies this weekend. 
  
• 머리가 아프거나 열이 날 때 이 약을 드세요. 
  => Take this medicine when you have either a headache or a temperature. 
  

(b) 

• 가라테나 태권도나 합기도를 배우고 싶어요. 
  => I want to learn karate or tae kwon do or hapkido. 
  
• 집이나 사무실로 연락 주세요. 
  => Please get in touch with me at home or at my office. 
  
• 방학 동안 한국이나 일본에 다녀오려고 해. 
  => During the vacation, I plan to visit Korea or Japan. 

This ending is used in casual and intimate conversation. It is a question when spoken with a rising tone and a statement when spoken with a level tone. 

• 내일 나하고 같이 나가 주지 않을래? 
  => Won't you go out with me tomorrow?
  
• 산에 같이 올라 갈래요?
  => Will you climb the mountain with me?
  
• 지금 밥 먹을래? 
  => Are you going to eat now?
  
• 안 먹을래.
  => I'm not going to eat.

This construction asks for permission in an informal and casual way. 

• 한국말로 물어도 돼요? 
  => May I ask you in Korean? 
  네, 물어 보세요.
  => Yes, go ahead.
  
• 지금 집에 가도 돼요? 
  => May I go home now? 
  가도 돼요.
  => Yes, you may.
  아니오, 가면 안 돼요.
  => No, you may not. 
  
• 숙제를 내일까지 내도 돼요?
  => Is it okay to turn in my homework tomorrow?
  네, 괜찮아요./네, 좋아요.
  => Yes, it's okay.
  
• 보고서를 연필로 써도 돼요?
  => May I write my report with a pencil?
  연필로 쓰면 안 돼요. 
  => You may not write with a pencil. 
  펜으로 써야 돼요.
  => You have to write in ink.
  

Notice the differences in the positive and negative answers:

• -(어/아)도 돼요? 
  => "Is it all right to . . . ?" 
  
• 네, . . . -(어/아)도 돼요.
  => "Yes, it's all right . . ." 
  
• 네, -(어/아)도 괜찮아요/좋아요. 
  => "Yes, it is fine."
  
• 아니오, . . . -(으)면 안 돼요. 
  => "No, (one) must not . . . ," "it should not . . . ,"

This sentence ending expresses the speaker's opinion and often translates into "I think . . ." in English.

• 내 눈으로 보는 것 같았다.
  => It was like seeing it with my own eyes. 
  
• 내가 밥을 너무 많이 먹은 것 같군요.
  => I think I ate too much.
  
• 비가 온 것 같았어요.
  => It looked as though it rained a lot.
  
• 곧 비가 올 것 같아요.
  => It looks as though it's going to rain soon.