Actually, it IS very easy:
you say:
It is a cat (pointing at the cat) and btw, you mean it's not a dog
but
There is a cat on the mat (you want to say what is on the mat)

next comes the plural form:
They are cats (once again - not dogs )
There are cats on the mats (there are many cats, at least more than one)

The construction "it's" can be be used much more widely:
It's raining/snowing
It's hot/warm
It's lovely/ugly

Almost all of them can be featured like that:

it's + a noun
it's + V (verb)ing
it's + adverb