Instrumental Case

When I just the 3rd person singular conjugation of the verb byc which is jest, do I change the do noun to make it have the ending with -em or -a. Or jest does not change the noun and it stays nominative?

Hmmmm... Which noun? Assuming you want to say 'this animal is a cat' == 'to zwierzę jest kotem' thie first noun stays nominative, the second does not.
Give an example.

Yes, as an example, ja jestem anglikiem-I am an Englishman, is in the instrumental case.

But if you say to jest tygrys. you don't add the -em because of the to but if you omit that, than you would add the -em like jest tygrysem.

Well, if you try to describe (or make it more specific) one nount with another there will be -em added to the describing noun (if this noun is masculine or neutral, otherwise it will be -ą). 'To zwierzę jest tygrysem' is equivalent to 'This animal is a tiger'- so you make it more specific. Remember, that even if you don't add explicitly a second noun in 'jest tygrysem', it is still there- this sentence efectively has two nouns- what you say is actually "On/ona/ono jest tygrysem"!

Just a small addition: the change from 'to jest tygrys' to 'jest tygrysem' is actually a change from 'this is a tiger' to 'he/she/it is a tiger'. Quite a big change, I'd say :).

The Instrumental Case ("narzednik", in Polish!) is funny. On the one hand, it's true that what seems to English speakers as pure nominative, e.g. the verb "to be", takes the Instrumental in Polish "Jestem Polakiem.", "On jest lekarzem.", "Czy Pan jest tlumaczem?" etc. The exception here is in more informal speech, such as "On nauczyciel, nieprawda?", without the verb 'to be' in the clause.

There are, by the way, a number of verbs which require the Instrumental Case, as other verbs require the Dative, Accusative or Genitive, which I frankly don't all recall, except, oddly enough, the verb "interesowac sie" = to be interested in

"Interesuje sie rolnictwem." = I am interested in agriculture

Like in German, in Polish, a case ending will be used without a preposition which would be necessary in English, for example, "to be interested IN" ....

Marek