Pusteteknikken er viktig.

Because -en is the usual definite singular ending for many common-gender nouns in Norwegian.

• en pusteteknikk = a breathing technique
• pusteteknikken = the breathing technique

So the noun itself carries the meaning of the.

The dictionary form is pusteteknikk.

A few useful forms are:

• en pusteteknikk = indefinite singular
• pusteteknikken = definite singular
• pusteteknikker = indefinite plural
• pusteteknikkene = definite plural

So if you look the word up, you would usually search for pusteteknikk.

Norwegian very often combines words into compound nouns.

So pusteteknikk is one compound word:

• puste = to breathe
• teknikk = technique

Together, they form pusteteknikk. This is very normal in Norwegian. English often writes similar ideas as two words, but Norwegian often prefers one.

In Norwegian, the definite article is usually attached to the end of the noun instead of standing in front of it.

So:

• the book → boken
• the breathing technique → pusteteknikken

A separate word such as den is used in certain situations, especially when there is an adjective before the noun:

• den viktige pusteteknikken = the important breathing technique

But in your sentence, there is no adjective directly before the noun, so pusteteknikken by itself is enough.

Er is the present tense of å være, which means to be.

So:

• jeg er = I am
• du er = you are
• han/hun er = he/she is
• de er = they are

Unlike English, Norwegian does not change the form of the verb depending on the person. It stays er.

Viktig is an adjective, meaning important.

In Pusteteknikken er viktig, it comes after er and describes the subject. So it is functioning as a predicate adjective or subject complement.

The structure is:

• Pusteteknikken = subject
• er = verb
• viktig = adjective describing the subject

This is the normal word order for a simple statement in Norwegian:

• subject + verb + complement

So:

• Pusteteknikken = subject
• er = verb
• viktig = complement

This is very similar to English The breathing technique is important.

It also fits the Norwegian V2 rule: in a main clause, the finite verb is in the second position. Here the subject comes first, so the verb naturally comes second.

Yes, and the meaning becomes more general.

• Pusteteknikken er viktig = the breathing technique is important
  This sounds like a specific breathing technique, or one already known from context.

• Pusteteknikk er viktig = breathing technique is important
  This sounds more general, like a general statement about breathing technique as a topic.

So the version with -en is more specific.

A rough pronunciation guide is:

PU-ste-tek-NIK-ken

A few things to notice:

• the u in pust is not like the English u in cut
• the e sounds are usually short and clear
• kk means the consonant is pronounced short and firm
• the final -en is unstressed

In compounds, the first part often gets strong stress, but teknikk also keeps noticeable stress in its own part. So the word has a natural compound rhythm.

For a question, move the verb to the front:

• Er pusteteknikken viktig? = Is the breathing technique important?

For a negative sentence, add ikke after the verb:

• Pusteteknikken er ikke viktig. = The breathing technique is not important.

These are very common patterns in Norwegian, so this sentence is a good model to learn from.