Foi um mau dia.

Foi is the preterite (simple past) form of the verb ser for he/she/it and you (formal você).

So in Foi um mau dia, foi means was.

A common point of confusion is that foi can also come from ir and mean went, but not here. In this sentence, it is clearly from ser, because it is followed by a noun phrase: um mau dia.

Portuguese often omits subject pronouns when they are not needed.

In English, you must say It was a bad day.
In Portuguese, you can simply say Foi um mau dia.

The idea of it is understood from context. This is very normal in Portuguese.

Both foi and era can mean was, but they are used differently.

• foi = completed event/state in the past
• era = ongoing, habitual, descriptive background in the past

So:

• Foi um mau dia. = It was a bad day.
  This sounds like you are summing up the day as a whole, as a completed past fact.

• Era um mau dia. = It was a bad day.
  This is possible in some contexts, but it sounds more like background description in a story.

For this sentence by itself, foi is the most natural choice.

This is one of the most common questions for learners.

• mau = bad (usually an adjective)
• mal = badly, poorly, or evil/harm depending on context

In Foi um mau dia, mau is correct because it describes the noun dia.

A useful shortcut:

• mau is often the opposite of bom
• mal is often the opposite of bem

Examples:

• um mau dia = a bad day

• um bom dia = a good day

• Ele dormiu mal. = He slept badly.
• Ele dormiu bem. = He slept well.

Because Portuguese normally uses an article here.

• um mau dia = a bad day

Leaving out um would sound incomplete or unnatural in normal speech.

So:

• Foi um mau dia. = natural
• Foi mau dia. = not normal standard Portuguese

Because grammatical gender does not always match the ending.

Most nouns ending in -a are feminine, but dia is a very common exception. It is masculine:

• o dia
• um dia
• bom dia
• mau dia

So mau and um are masculine to agree with dia.

In Portuguese, adjectives often come after the noun, but some can also come before it.

Mau often appears before the noun in common expressions like:

• um mau dia
• um mau aluno
• um mau exemplo

With dia, um mau dia sounds natural and standard.

In general, adjective placement in Portuguese can sometimes affect style or emphasis, but here you should simply learn um mau dia as a normal phrase.

Yes. In Brazilian Portuguese, ruim is very common and often sounds more natural in everyday speech.

So these both work:

• Foi um mau dia.
• Foi um dia ruim.

The second one is often more common in casual Brazilian Portuguese.

A small difference:

• mau can sound a little more formal, literary, or fixed
• ruim is very common in everyday conversation

A simple approximate pronunciation for an English speaker is:

foy oom mow JEE-ah

A few details:

• foi sounds roughly like foy
• um in Brazilian Portuguese often sounds nasal, something like oom with a nasal quality
• mau rhymes roughly with English now, but starts with m
• dia is usually JEE-ah in Brazilian Portuguese

In natural speech, words may connect smoothly, so it can sound a bit like:

foy um mau jia

Yes, it is correct and natural. However, in everyday Brazilian Portuguese, many speakers would more often say:

• Foi um dia ruim.

So Foi um mau dia is perfectly good Portuguese, but Foi um dia ruim may sound more conversational in Brazil.

Yes. Foi can come from two different verbs:

• ser = to be
• ir = to go

So foi can mean either was or went, depending on context.

Examples:

• Ela foi professora. = She was a teacher.
• Ela foi ao mercado. = She went to the market.

In Foi um mau dia, it can only mean was, because um mau dia is not a destination or place.

Word-for-word, yes, that is roughly what the Portuguese structure looks like. But in natural English, you need it:

• It was a bad day.

This is a good example of how Portuguese often leaves out subjects that English requires.