1. 생각하다 : think
ex) I think it will be expensive : 난 그게 비쌀 거라고 생각해
But when the past tense (thought) is used, 알았다(knew) can replace 생각했다.
ex) I thought it would be expensive : 난 그게 비쌀 줄 알았어/난 그게 비쌀 거라고 생각했어
2. -는 것 같다 : in between think and find
ex) I think it's interesting : 그거 재밌는 것 같아
ex) I find him attractive : 그 남자 매력 있는 것 같아
3. -던데/-은데/-더라(고) : find
Usually -던데/-은데 is used to show a little disagreement with previous statements or to ask what others feel about the statement being spoken.
ex) That movie was so boring / But I found it fun : 그 영화 너무 지루했어 / 그래도 난 재밌었는데
ex) I found him handsome / Really? He looks ugly to me : 그 남자 잘생겼던데? / 진짜? 나한텐 못생겨 보여
-더라(고) is a little more focused on expressing opinion than -던데/은데 and usually refers to past events.
ex) I was unwilling to do it, but I found it fun in the end : 마지못해 했었는데 나중에는 재밌더라고
All of -던데, -은데, -더라(고) sound a little informal. You can use them when speaking with a stranger, but you should not during an interview. And as for -던데/-은데, they have meanings other than "find" so you should check them out.
4. 보다/믿다 : believe
보다 is in somewhere between "think" and "believe", and it implies that the opinion might change or turned out false. 믿다 expresses stronger belief than 보다.
ex) I think/believe you should break up with her : 난 너가 걔랑 헤어져야 한다고 봐
ex) I believe something good will happen : 좋은 일이 일어날 거라고 믿어
If you want to use these words more naturally, you can consider the things below:
If you don't omit the subject ("난/나한텐" in some examples above), the sentence sounds like the opinion is peronal and other people can think differently, so it makes the sentence express the feeling less stronger.
You can combine 1/4 with 2/3. For example, you can say '난 그거 재밌는 것 같던데' by using both 2 and 3. And this makes the sentence less stronger, too.
When you state other people's opinion, you have to add '-아/어/해하다' in the sentence. For example, you have to use "걔 그거 싫어하던데", not "걔 그거 싫던데" for "He/She seems to hate it."