When should I use "很" before an adjective? Very early in the process of learning Chinese as a foreign language we are taught:


我是好 is incorrect because 是 is only used before nouns and 好 is not a noun.
我很好 is the correct way to say the former
很 literally means "very" but in this type of usage doesn't have this literal meaning.
很 isn't always used between a noun and an adjective


(This naturally results in some foreign learners thinking of 很 as some kind of special equivalent to "to be".)

But when should we use 很 and when should we omit it? In some other places in Chinese grammar we use some character with monosyllabic words and omit it with bisyllabic words. I'm not sure if that's the case here though since I'm sure I've seen 很 used with both monosyllabic and bisyllabic words.
Yes.It is common for "很" to be used before both monosyllabic and disyllabic adj. But when these types of adj./adv. are used, the front "是"are always omitted. For example，我很优秀（I am excelent）, 我的国家很强大（My country is powerful). This mechanism covers most  of the context. But you may use 我是很优秀，or 我的国家是很强大。It is not grammatically incorrect,but you will hold a tone of sarcasm (or at least a serious tone),so there's smaller chance to use this format . 

When the speaker uses 我是很好,我是很优秀 or 我的国家是很强大。He/She wants to express the determined tone to the recipient,in which he/she consolidates his/her authority,or against others' questioning for the most of the cases. In other words,he/she is boasting or even be conceited about the advantages of his/her or his/her contry.