Vi vil adoptere en hund.

• Vi = the subject pronoun, we
• vil = the finite verb here; it is a modal verb
• adoptere = the main verb in the infinitive, to adopt
• en = the indefinite article, a
• hund = the noun, dog

So the structure is:

subject + modal verb + infinitive + article + noun

It can mean either, depending on context.

• As a main idea, å ville often means to want
• In some contexts, vil can also help express the future, similar to English will

So Vi vil adoptere en hund can mean either:

• We want to adopt a dog
• We will adopt a dog

In real life, context tells you which meaning is intended. If Norwegian speakers want to make a simple future sound more natural, they also often use skal.

Because after a modal verb, Norwegian normally uses the bare infinitive.

That means:

• vil adoptere
• kan adoptere
• skal adoptere
• må adoptere

not:

• vil å adoptere

This is similar to English:

• we want to adopt but
• we will adopt

After Norwegian modal verbs, the infinitive usually appears without å.

Adoptere is the infinitive form of the verb.

The dictionary form is å adoptere.

Some common forms are:

• å adoptere = to adopt
• adopterer = adopt / adopts / am adopting / is adopting, depending on context
• adopterte = adopted
• har adoptert = have adopted / has adopted

So in your sentence, adoptere stays in the infinitive because it follows the modal verb vil.

Because hund is a common-gender noun in Bokmål, so it takes en in the indefinite singular.

• en hund = a dog
• hunden = the dog
• hunder = dogs
• hundene = the dogs

A lot of English speakers wonder whether they can guess noun gender. Sometimes you can, but often you simply have to learn the noun together with its article:

• en hund
• et hus
• ei bok or en bok, depending on style

Because en hund is indefinite and hunden is definite.

• en hund = a dog, any dog, not previously identified
• hunden = the dog, a specific dog already known from the context

So if you are just introducing the idea for the first time, en hund is the natural choice.

Yes. This is a normal Norwegian main-clause pattern:

subject + finite verb + rest of the sentence

Here that gives:

• Vi = subject
• vil = finite verb
• adoptere en hund = rest of the verb phrase and object

Norwegian is a V2 language, which means the finite verb usually comes in the second position in main clauses.

So if you move something else to the front, the verb still stays second:

• I morgen vil vi adoptere en hund

not:

• I morgen vi vil adoptere en hund

Usually ikke comes after the finite verb and before the infinitive/main verb.

So:

• Vi vil ikke adoptere en hund = We do not want to adopt a dog / We will not adopt a dog

This placement is very common with modal verbs:

• Jeg kan ikke komme
• Hun skal ikke reise
• De må ikke vente

Yes. That is also correct, but it has a slightly different feel.

• Vi vil adoptere en hund can mean we want to adopt a dog or we will adopt a dog
• Vi ønsker å adoptere en hund more clearly means we wish to adopt a dog or we would like to adopt a dog

So ønsker å can sound a bit more explicit or formal than vil.

A rough guide is:

• Vi ≈ vee
• vil ≈ vil with a short i, somewhat like the vowel in sit
• adoptere ≈ ah-dop-TEH-reh, with the stress on te
• en is often weak and short
• hund has a Norwegian u sound that does not match English perfectly

A more phonetic version in IPA is roughly:

/viː vil adʊpˈteːrə ən hʉn/

The hardest part for many English speakers is hund. It does not sound like English hound. The vowel is shorter and more rounded.