Tränaren fixar problemet.

Because tränaren is the definite singular form of tränare.

• en tränare = a trainer / a coach
• tränaren = the trainer / the coach

In Swedish, the definite article is often added to the end of the noun instead of being a separate word like the in English.

The base form is tränare.

So you have:

• tränare = trainer, coach
• en tränare = a trainer, a coach
• tränaren = the trainer, the coach

This noun belongs to the en-word group, which is why the definite ending is -en.

Because problemet is the definite singular form of problem.

• ett problem = a problem
• problemet = the problem

This noun is an ett-word in Swedish, so the definite ending is -et.

In Swedish, the is very often built into the noun itself.

So instead of saying something like the trainer with a separate article, Swedish commonly says:

• tränaren = the trainer
• problemet = the problem

This is one of the biggest differences from English noun structure.

Fixar is the present tense of fixa.

• att fixa = to fix, sort out, solve, arrange
• fixar = fixes / is fixing / sorts out

So Tränaren fixar problemet is in the present tense: The trainer fixes / is fixing the problem.

Because Swedish verbs do not change according to the subject the way English verbs sometimes do.

In English:

• I fix
• he fixes

In Swedish, the present tense stays the same:

• jag fixar
• han fixar
• hon fixar
• de fixar

So fixar works for all persons in the present tense.

Not always. Fixa is a very common everyday verb, and its meaning depends on context. It can mean:

• fix
• solve
• sort out
• arrange
• sometimes even repair

In Tränaren fixar problemet, it often feels natural as The trainer solves the problem or sorts out the problem, not only fixes the problem in a mechanical sense.

It can mean both, depending on context.

Tränare is often used for:

• a sports coach
• a physical trainer
• sometimes an instructor in training contexts

So if this sentence is about sports, the coach may be the most natural translation.

The word order is:

subject + verb + object

• Tränaren = subject
• fixar = verb
• problemet = object

This is the normal basic word order in Swedish statements, just like in English:

• The trainer
  • fixes
    • the problem

Yes, but Swedish has special word-order rules. In a normal statement, subject + verb + object is the most basic pattern.

You can move another part to the front for emphasis, but then the verb still usually stays in the second position. For example, with a time word:

• Idag fixar tränaren problemet. = Today, the trainer fixes the problem.

This is part of Swedish V2 word order.

The letter ä is pronounced somewhat like the e in bed, though exact pronunciation depends on accent and dialect.

So tränaren is roughly like:

• TREH-na-ren

That is only an approximation for English speakers, but it helps. The important thing is that ä is not pronounced like English a in train.

Because everything here is singular:

• tränaren = the trainer (one person)
• problemet = the problem (one problem)

If the sentence were plural, the nouns would look different. For example:

• tränarna = the trainers
• problemen = the problems

In this sentence, word order tells you that:

• Tränaren comes before the verb, so it is the subject
• problemet comes after the verb, so it is the object

Also, semantically, it makes sense that the trainer is doing the action and the problem is receiving the action.

So:

• Tränaren = the one who acts
• problemet = the thing being dealt with

The indefinite forms are:

• en tränare = a trainer / a coach
• ett problem = a problem

The sentence uses the definite forms instead:

• tränaren = the trainer
• problemet = the problem

Learning both the indefinite form and the definite form together is very useful in Swedish.