Træningsprogrammet begynder med opvarmning og slutter med udstrækning.

Because Danish often puts the definite article at the end of the noun as a suffix.

• træningsprogram = training program
• træningsprogrammet = the training program

This is called the suffixed definite article.

You can also use det træningsprogram, but that usually needs something extra after it, such as a description:

• det træningsprogram, jeg bruger = the training program that I use
• det nye træningsprogram = the new training program

So in your sentence, træningsprogrammet is the normal standalone way to say the training program.

The ending -et is the definite article for many neuter nouns in Danish.

Here:

• et træningsprogram = a training program
• træningsprogrammet = the training program

Danish nouns usually have one of two genders:

• common gender often takes -en in the definite form
• neuter gender often takes -et in the definite form

Since træningsprogram is a neuter noun, it becomes træningsprogrammet in the definite form.

Because in this sentence they are being used as general activities, not as specific individual things.

So Danish says:

• med opvarmning = with warm-up / with warming up
• med udstrækning = with stretching

This is similar to English, where you might also say:

• The session starts with warm-up and ends with stretching

If you wanted to refer to a specific warm-up or a specific stretching routine, an article could appear in some contexts, but here the general activity is what matters.

In Danish, begynde med and slutte med are very common patterns meaning:

• begynde med = begin with
• slutte med = end with

So the sentence structure is very natural:

• begynder med opvarmning
• slutter med udstrækning

This matches English quite closely. It is simply the preposition these verbs normally use in this meaning.

Because begynder and slutter are the present tense forms.

The basic verb forms are:

• at begynde = to begin
• at slutte = to end

Present tense:

• begynder = begins
• slutter = ends

So:

• Træningsprogrammet begynder ... = The training program begins ...
• Træningsprogrammet slutter ... = The training program ends ...

A useful thing to notice is that Danish present tense verbs do not change according to the subject. The same form is used with jeg, du, han, vi, and so on.

The sentence follows normal Danish main clause word order:

Subject + verb + other elements

• Træningsprogrammet = subject
• begynder = verb
• med opvarmning = prepositional phrase
• og = and
• slutter med udstrækning = second coordinated verb phrase

So the structure is:

Træningsprogrammet begynder med opvarmning og slutter med udstrækning.

This is very similar to English word order in this kind of sentence.

Yes, in this sentence og works just like and.

It links two parallel parts:

• begynder med opvarmning
• slutter med udstrækning

Both parts describe what træningsprogrammet does.

So Danish avoids repeating the subject:

• Træningsprogrammet begynder ... og slutter ...

just like English:

• The training program begins ... and ends ...

In this sentence, they are nouns.

• opvarmning = warm-up / warming up
• udstrækning = stretching

They are formed from verbs:

• at varme op = to warm up
• at strække ud = to stretch

Danish often uses these -ning nouns to talk about activities in a general way.

Compare:

• Vi starter med at varme op. = We start by warming up.
• Vi starter med opvarmning. = We start with warm-up.

Both are natural, but the version in your sentence sounds a bit more like describing the structure of a program.

Yes. A very common alternative would be:

Træningsprogrammet starter med opvarmning og slutter med udstrækning.

Here, starter is often used in everyday speech instead of begynder.

Another natural option is:

Træningsprogrammet begynder med at varme op og slutter med at strække ud.

This version uses verb phrases:

• at varme op = to warm up
• at strække ud = to stretch

Your original sentence is completely natural, but it sounds a little more formal or structured, which fits something like a training plan or written instructions.

A learner will often notice these letters:

• æ in trænings-
• y in begynder
• ø in begynder

Very roughly:

• æ sounds somewhat like the vowel in English cat, but not exactly
• y is a front rounded vowel that English does not really have
• ø is also a front rounded vowel, also unfamiliar to most English speakers

A few rough pronunciation notes:

• træning starts with something like treh-
• begynder has two difficult vowels for English speakers
• udstrækning contains æ again

The biggest tip is not to rely too much on English spelling instincts. Danish pronunciation is less phonetic than it looks, so it helps a lot to hear native audio and repeat whole words rather than sounding them out letter by letter.

No. Opvarmning can also mean heating or warming in other contexts.

For example:

• opvarmning af huset = heating of the house
• opvarmning før træning = warm-up before training

So the exact meaning depends on context. In your sentence, because of træningsprogrammet, it clearly means a physical warm-up before exercise.

They are closely related, but they are different grammatical forms.

• udstrækning = a noun: stretching
• at strække ud = a verb phrase: to stretch

So:

• Programmet slutter med udstrækning. = The program ends with stretching.
• Programmet slutter med at strække ud. = The program ends by stretching.

Both are natural. The noun version is often a little more compact and fits well in descriptions of schedules, routines, and programs.