Sounds very easy so far, right? Here comes the pain-in-the-ass part. Trust me, even Korean native speakers really cannot distinct them clearly and use them wrongly in daily life without attention. 

You may have come across examples like: 

1. 이것은 집이에요.  2. 저것은 바다예요.  3. 이것은 술이 아니어요. 

… … what!!! Why???

First thing, keep in mind‘-이에요/-이어요' is the standard form! Here,  '이' is a particle, which is used when you are speaking about subject and '-에요/-어요'is the ending of the sentence. (By the way, there is no significant difference between -이에요 and -이어요)

Therefore, you need to know they combine with nouns (case A, case B); or they can be in the middle of one phrase directly (case C): 

B. Nouns without 받침

나무+-이에요/-이어요 → 나무이에요/나무이어요 → 나무예요/나무여요. 

As you can see, in this case, both '나무이에요' and  '나무이어요' has turned into the shortening form '나무예요' and '나무여요'. This is the reason why -예요,-여요 exist, they are variables from  -이에요, -이어요. In daily life, '나무예요' is commonly used by native speakers. Therefore, just remember '-예요' when it comes to the nouns without받침 . 

C. When they are combined with adj,  used in the middle of one phrase/sentence, 

'이' should be taken away from here, which means‘-이어요/-이에요' turns into '-에요/-어요'.

'아니다' is a representative example.

Similarly, ‘아녜요/아녀요’is the shortening form of 아니에요/아니어요. Among these, '아니에요' and '아녜요' are used frequently. We use '아뇨' casually when we type, too. 

 

To sum up, the golden rule is that: 

Right! hope this makes sense to you all! ; ))