When "to be" should be used? When omitted? There are cases in which "to be" is translated with 是 ( shì ), while in some other cases it seems not to be translated at all.
When should 是 ( shì ) be used? When omitted?

Here some examples:
我很好
wo hen hao 
 I am very well

我是英国人
wǒ-shì-yīng-guó-rén
I am English

Wo hen kuai le
我 很快乐
I'm happy

我 25 岁 了
Wǒ èrshíwǔ suì le
I'm 25 years old

Disambiguation 1: I landed in a similar question: When should I use the 是...的 construction? 
Note that it addresses the usage of 是 and的 !

Disambiguation 2: This question has been marked as oossible duplicate of: Why is (是) shi4 dropped in this sentence：&quot;我很好&quot;?

Indeed the subject is similar. I think that this question is more General, while the other targets a specific case (I was not able to find it before posting my question!). To be noted that some answers are quite similar.
是 in the first context is only used to say:

Noun1 是 Noun2

You never say 我是很好, because 好 isn't a noun. You can say

我是美国人
他是男孩子
我是李红

because all those relate one noun to another. In the case of 我25岁了, 25 years old isn't a noun, it's a state, and so we don't use 是.
For a simple summary, 是 only relates 2 nouns to each other. If it's not a noun, don't use 是.
You can find more info and examples here, which I find is a good site for beginners to learn chinese, and gives lots of examples to help you understand.