Jeg blev glad, da min ven kom.

Blev is the past tense of blive, which often means become.

So Jeg blev glad means I became happy or I got happy. It focuses on the change of state.

If you said Jeg var glad, that would mean I was happy, describing a state rather than the moment the feeling started.

Both are in the simple past.

• blev = past of blive
• kom = past of komme

So the whole sentence is talking about something that happened in the past:
I became happy when my friend came.

Here da means when and refers to a specific event in the past.

In Danish:

• da = when, for a one-time event in the past
• når = when, for repeated events, general truths, or future meaning

So in this sentence, da min ven kom means when my friend came on that particular occasion.

Because da introduces a subordinate clause.

In Danish subordinate clauses, the subject usually comes before the finite verb:

• da min ven kom = when my friend came

If you say da kom min ven, that would sound like main-clause word order, which is not correct here.

So the pattern is:

• da
  • subject + verb

Because min already makes the noun definite.

In Danish, possessives like min, mit, mine work like this:

• min ven = my friend
• not min en ven
• not min vennen

So min ven is the normal correct form.

Because ven is a common-gender singular noun.

Danish possessives change depending on gender and number:

• min for common gender singular
• mit for neuter singular
• mine for plural

Examples:

• min ven = my friend
• mit hus = my house
• mine venner = my friends

So ven takes min.

Here glad is a predicative adjective: it comes after blev and describes the subject jeg.

With jeg referring to one person, the normal form is glad.

Compare:

• Jeg blev glad = I became happy
• Barnet blev gladt = The child became happy
• De blev glade = They became happy

So the adjective can change, but with jeg here, glad is the correct form.

Yes. That is the most literal translation.

But in natural English, people often say:

• I was happy when my friend came
• I got happy when my friend came
• I was glad when my friend came

The exact English wording may vary, but the Danish blev clearly suggests a change: the speaker became happy at that moment.

Because da min ven kom is a subordinate clause.

In standard Danish writing, a comma is commonly used before subordinate clauses like this:

• Jeg blev glad, da min ven kom.

So the comma helps separate the main clause from the da-clause.

Yes. You can also put the da-clause first:

• Da min ven kom, blev jeg glad.

That still means the same thing.

Notice what happens in the main clause after the fronted subordinate clause:

• blev jeg glad
  not jeg blev glad

This is because Danish main clauses follow verb-second word order.

No. Ven can mean friend in a general sense and does not have to mean a male friend.

If you want to be explicitly feminine, Danish also has veninde for female friend, but ven is often used broadly depending on context.

So min ven can simply mean my friend.