1. 그리고 (geu-ri-go) - And
Use this conjunction to add additional information. For example, if you wanted to say:
Do you want to watch a movie together? And let's have dinner.
같이 영화 볼래? 그리고 저녁 먹자.
2. 하지만 (ha-ji-man) - However
Let's look at an example: I called my friend however he didn't hear me.
You could say: 나는 친구를 불렀다 하지만 친구는 나를 듣지 못했다.
But this is a little too long right? Then you can use: verb+지만 (~ji-man)
So, instead you could say: 나는 친구를 불렀지만 친구는 나를 듣지 못했다.
3. 근데 (geun-dae) - But
This is a synonym to 하지만 and can be used in it's place. It can also be used at the beginning of a sentence to mean: By the way...
Let's take a look at this example: By the way, I called my friend but he didn't hear me.
You could use 근데 instead of 하지만: 근데, 나 친구를 불렀다 근데 친구는 나를 못 들었어.
But this is a little too long right? Then you can use: verb+는데 (~neun-dae)
So, instead you could say: 근데, 나 친구를 불렀는데 친구는 나를 못 들었어.
4. 아니면 (a-ni-myeon) - Or
If you want to say or, use the conjunction 아니면.
Let's take this example: Do you want coffee or tea?
You could say: 커피 마실래 아니면 차 마실래?