Japanese sentences

Some japanese people often leave sentences unfinished in conversation, like saying 'でも…' or 'それはちょっと…' without completing the thought. How do i know when it's appropriate to do this, and how can i use it naturally in my own speech?

I don't think it is something that can be taught academically. It is something that you pick up in conversation with Japanese people, or possibly something you can learn from watching movies, dramas, and maybe some other shows. A large part of Japanese language is unspoken, inference. So the speaker can omit some parts of speech, and still be understood.

Hard for foreigners to do this naturally, because our (foreigners) thought and speech patterns are different.

That makes sense! I guess a lot of it comes down to feeling out the flow of conversation and understanding cultural nuances rather than just learning grammar rules. Tough it's harder for foreigners, it's worth to at least get a sense of when it feels natural. Could you please tell me how it's used when you're trying to say no without actually saying no??

If your friend invites you out somewhere, you can demur by saying いえ、ちょっと which implies you don't want to go out, without specifying the reason. Its more polite than saying, "I don't want to go out" or "I don't want to do that thing".

Your acquaintance is showing you a kindness, and it would be rude to just reject it by saying "I'm not interested". So instead you just decline by いえ、ちょっと (implying that you are busy on that day).

But this requires a pretty good degree of fluency to just toss out this phrase and have it be accepted. Also, your friend might continue to push you and ask you why you can't make it.

Or, if you are out eating with friends, and they ask you if you like (for example) sushi. If you don't like sushi, you can say,
いえ、ちょっと, again, implying you don't like it in a roundabout way. Its more polite than saying いえ、きらいです which would be a logical and acceptable answer in English - but in Japanese it feels harsh and could be rude depending on the context.