Jeg havde lidt besvær med at få låget af, så min nabo hjalp mig.

Because the sentence is in the past tense.

• har = have / has
• havde = had

So Jeg havde lidt besvær ... means I had a little trouble ...

The second verb is also in the past:

• hjalp = helped

That tells you the whole situation happened in the past.

Here lidt means a little or some.

So:

• lidt besvær = a little trouble / some difficulty

It often softens the statement, just like English a bit:

• Jeg havde lidt besvær = I had a bit of trouble

It does not necessarily mean the problem was tiny; it can simply make the sentence sound more natural or less dramatic.

Besvær means trouble, difficulty, or hassle.

In this sentence:

• Jeg havde lidt besvær med at få låget af = I had a little trouble getting the lid off

A useful thing to know is that besvær is often used as an uncountable noun, much like trouble in English:

• have trouble
• have difficulty

So Danish says:

• have besvær med noget
• have besvær med at gøre noget

Because Danish often uses the pattern:

• besvær med at + infinitive

This means trouble/difficulty doing something.

So:

• besvær med at få låget af = trouble getting the lid off

Word by word, it is closer to:

• trouble with to get the lid off

That sounds strange in English, but it is normal in Danish.

You will see the same pattern in many sentences:

• Jeg har problemer med at sove = I have trouble sleeping
• Han havde svært ved at forstå det = He had difficulty understanding it

Få låget af literally means get the lid off.

This is a very natural Danish way to talk about removing something:

• få hætten af = get the cap off
• få skoene af = get the shoes off
• få etiketten af = get the label off

So in this sentence, the focus is not just on opening, but specifically on removing the lid.

That is why få ... af works well here.

Here af means off.

It belongs with the idea of removal:

• få låget af = get the lid off

In English, off is also often placed at the end:

• get the lid off

So this part is actually quite similar between the two languages.

Danish often uses short particles like this:

• tage skoene af = take the shoes off
• skrive det ned = write it down
• slukke lyset = turn off the light

Because låget is the definite form, meaning the lid.

The noun is:

• et låg = a lid

Its definite form is:

• låget = the lid

This is a key feature of Danish: the definite article is often added to the end of the noun.

Compare:

• en bog = a book

• bogen = the book

• et glas = a glass
• glasset = the glass

So:

• få låget af = get the lid off

Because after a possessive like min, Danish normally uses the indefinite form of the noun.

So:

• min nabo = my neighbor

Not:

• min naboen

This is similar to English, where we say my neighbor, not my the neighbor.

Compare:

• min bil = my car
• mit hus = my house
• mine venner = my friends

Here så means so or therefore.

It connects the two parts of the sentence:

• Jeg havde lidt besvær med at få låget af
• så min nabo hjalp mig

Together:

• I had a little trouble getting the lid off, so my neighbor helped me.

This så is not the same as så meaning then or like that in other contexts. Danish så has several uses, and here it is the logical connector so.

Because in this sentence så is being used as a conjunction meaning so, linking two main clauses.

So the normal word order is:

• så min nabo hjalp mig

That is:

• so my neighbor helped me

If så were being used more like an adverb meaning then, you could get inversion:

• Så hjalp min nabo mig = Then my neighbor helped me

So the version in your sentence is natural because så is functioning as a connector between the two clauses.

Yes. Hjælpe (to help) is irregular in the past tense.

Its forms are:

• hjælpe = to help
• hjælper = help(s)
• hjalp = helped
• har hjulpet = has/have helped

So:

• min nabo hjalp mig = my neighbor helped me

This is a verb worth memorizing because it is common.

Because mig is the object form of the pronoun.

• jeg = I
• mig = me

In the sentence, the neighbor is doing the action, and me is receiving it:

• min nabo hjalp mig = my neighbor helped me

So:

• subject form: jeg
• object form: mig

Compare:

• Jeg hjalp ham = I helped him
• Han hjalp mig = He helped me

Yes, absolutely. A very common alternative is:

• Jeg havde lidt svært ved at få låget af

That also means:

• I had a little trouble getting the lid off

Both are natural, but they feel slightly different:

• have besvær med at ... = have trouble with ...
• have svært ved at ... = find it difficult to ...

In everyday speech, svært ved is extremely common.

Yes, it sounds natural and idiomatic.

Especially natural features are:

• lidt besvær = a normal way to say a little trouble
• med at få låget af = a very Danish way to say getting the lid off
• så min nabo hjalp mig = a straightforward everyday continuation

A native speaker would understand it immediately, and it does not sound overly formal or unnatural.